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;_Ts$ :i@Rr[ZRrBcs2"h~n%R5 qMk dFh6sQ{{/mB3(mn ]WWD>DQEF|WsotwcIŔ;0Ndva"{hS&.ZdMDD"qlO !9FX<k9N jjHɅKY%dOgA(D8,/xTSu_7Z` 3+ăLO_&Z)OAg}V2SqVFi1@GW RT&rKzes_JS4eG۲/n$'"BE2•u"dwL$w㔕d׫2982l,p#R4*R&C<3<{#[$"d_sM-U mUy*D9f 8̈(/ئ`\DG:F4>Xgӹް 4Ux d1(5}|-(&T:AQ9J87_-JWsԥ*G> endobj 456 0 obj [ 250 278 500 500 500 500 500 500 500 500 500 500 333 333 570 570 570 500 930 722 667 722 722 667 611 778 778 389 500 778 667 944 722 778 611 778 722 556 667 722 722 1000 722 722 667 333 278 333 581 500 333 500 556 444 556 444 333 500 556 278 333 556 278 833 556 500 556 556 444 389 333 556 500 722 500 500 444 394 220 394 520 0 0 0 333 500 500 1000 500 500 333 1000 556 333 1000 0 0 0 0 0 0 500 500 350 500 1000 333 1000 389 333 722 0 0 722 0 333 500 500 500 500 220 500 333 747 300 500 570 333 747 333 400 570 300 300 333 ] endobj 457 0 obj <> endobj 458 0 obj <>stream %!PS-AdobeFont-1.0: NimbusRomNo9L-Medi 001.005 %%CreationDate: Thu Nov 17 1994 % Copyright URW Software, Copyright 1994 by URW % URW Software, Copyright 1994 by URW 11 dict begin /FontInfo 10 dict dup begin /version (001.005) readonly def /Notice (URW Software, Copyright 1994 by URW) readonly def /Copyright (Copyright URW Software, Copyright 1994 by URW) readonly def /FullName (Nimbus Roman No9 L Medium) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Bold) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /UMGKCM+NimbusRomNo9L-Medi def /PaintType 0 def /FontBBox {-168 -218 1000 948} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec oc;jtD[1ƅpTo9`.:ypJ*l'e}#)&7+/^ W{LZ60VQR^λ3r)#v$p~c&'ſ+ %;a~!ty`rcv7pUupZJC.dMf*/+X.կmMV]BmDQuұGq!Ut 705/J3(g-Kx4z=25Ϥb~5N>e:9ۚzڥݪ<Eu':L9z(bǘ@;)Xb:ȥ"ޟ:-j y iޖXg-=׃.ԥL+FCe2_0E=o Qp*9g5 [8^qK9lAD1mLs_C&t''di݅hhYT^^ໜ5 ?cnd(/FL˄_DD%JFXuzN4}7X6'z;|.cm%R[2g:bWԍƟfu0g}`=m9UDX8 I>ٙ荖6<E `i*"tzreɼwPn-eAw9.q]oXJ-#Ov1lC~^RX J^c{A5' RAaEy➌:3Ch1}A(g^C 7Ap;c~@H|tE<5qRIsJ-j?+A}t|]>^Ժ6mwjѰd-)d;Z]d?/03l' |u.#ֹxI2743_GO~^_#++&8׀\q|xU?-y.9Һ'8Xm? <Ӣ;>ρ"<}3S*тy"["5?0P죶N2{V ȣ锩qXzE&@#};@UWaAKa۵sw#alg/-8<y֩M84'5{k%K1vjyc1#ݚWX@==-9(,ԉL0AtJĮAn*f\`P<pAei[mKvиPP[aׅVYj/ݑ:ªFŢ;T"6EԪ^-aU掏l?ћD)RQ/@j~ S$8p\Mkz8@p -l{Fagѫt+SʲL}YIJKGg4,N?J XOe) INfBj+2簫s&])`mZLWELߎśy;WNG^15$a IO5y/A&('Su]CƪRؖzEC#M#9i"į8? 1Cd:\suѿ(ZbA:Hqh!6md?Ae4Sem)L2Μ0ڷc\Si3@ Yxג|;%Q;odL0S@;zQdYJtPf/!6hQPS5U&\fѾ}0<`8=$r90 :n^,J;m|ըi]~IoUtj㻞uk6@&/EЫZᬈ_ IיTSavABʹa^,~fj پoGmh6ht/K"NhWxLF%[r VWc>8 SrYGWG'7N-Z~CJ.u o C& ̈́EUB$T|/y'9#){QSy)U2~g6\rנgۅ6noa"Q*  jk:?yuض??<`\ey+=k!|UI̗{;an',%FX-ofnf:TɗO<÷XRr/E-;s:f}. 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[´>I]51IWi?wA Wr440=AXn8kzWk ޑ|Y|K< @ ڧ. g*j5Ϛt,c#5i%=踦}畳8[iq6<8rų_ .\)b. b6u`dPlnܓ HaGx>xi ,jؽѣvRNcj*jᄑ m=a'cn&҃y Ru'LVpͬMmd |!RP[~kouv8{ )ْFLRt2^X l,})YD.i.JlH2'(cږ*[,Dg91i2F?*uA`ƎڶwꖀpAYy؝eto>ȂX"R & a`EXGJZg "Nm]]Zt5 VhAab;z$E5E|X}p7fCK+NUXmJm  " $  cg"vK1!D,[ s{2 e!wM#"nRbnnq bcaD):哿YN.|U:9{FJa_|UGw(=_N Oh(HΠ$GvC$R.GC3` yԲm7$Hʎծ_eؤ>4p ~ xuri>sĀ$FUM莛Vi1S߅S!>MuWXm _xY>%u==;cܐ=Gρ0=:;M:DZ@{sS0&Aɻ#3[њʭ'=§'-?<~>AT~8[LQ؋N+!plbлB32@ϳk(ׂc;QM,U͐}39K/Y=pȃfE5 354_uy3_K̐MЃ ¯x%)'t~13OC7pד@8Rabak;|_>'Lx4F鍤5I~1ɖ%WR/ ͎92u>=\.$MUVf큉@%h1Љ^XY{aj# r,z`H+P5$MwS}ډ^zE& ƦO!'Z€͜GSCz9Gc^uv(q5p-dד.jB DRSi9-3=zXn9SHsVaMQ qrBG:VHʣs&g JKt7p SIejwl ?'""(<1PI^ ->ɲ*.vբ(v+7ڴDz屷}ʴʈ_ݟ?|M6ĉf{蛰쳢س,*#=7൷!~ݦ= /-MҸP[G2/Mƿ&t XˢLGJ+~|uʆʐym 8ֺޏ,ನ U !X,h-j:#y3h2"n~l ]Ek+U`7{BOv d [cyrǎCQcYonItL1}y}Ӄ®䶎 Zh raW:U|"_+ΦJ y3r[WJ4/["Nf-fu$MAk,>T;kF^$dtdLaT襳mZ-E9MscʫEQ"RMgbj{1 ՜h[hl}G{^wV÷̓>$ĿO+u&!=$<exg 5:)zH3Iu[ygsߛәfӀb}h|X$u # l>i ߎ2{'0StAz˘WoHOv\$lN;;cS0x3|$2giɌ",vDeK3&z^X9N oE|x vt.vdy(-<eGO ?DIKC 6UgAYRT[EhIKه̶i>٭/̰㲵߱ .TΚYgƁ1>.$΅6e1# .x= 6 增`hהI`ȳmfYf Y[[H6Uk)l"`6q8FWi[vږ?5K[KcB #?ںc6OXЊΠG14fMK%? (9iXMЬ+NQ^TBlA*ak~QS:Kd#PkeȆ!|Nl]9~6T0 ; $+*]KjwxO^zNz:_ʭgu͗7beP#F?RPh˘n2eDr(䄿HyQށ]-VC@l&XlANή?8cl %?EW><& ̊}\BjZ:^ʄe ‰ TۦST8@qc4TĘ㌅( fzN ]+dnsAz.ޢ23sTO=+!Zta`tYkQumO"*{N[< )5P=(p{F݌Y~˹Wx6Tj:)`,!"ӝGJ]B};ǟr*wW[!n:R׬PEfEi%6ͬR-ǧj* u Tq``jm +ݜt y$(XA|ɤ?㕙PI9Ō:OLpL1:O\`RXFBR@ӍFrr}JUKY̿>zLȑ8I:Yi{t9L.&ǁ"ݗɱt{LU E QtZtPDx8 f M,:ڋ~ֶM^PNxV)c[ke"YZ[I8$TYy[>t/8 vX$ǑHCӵR/BA!aLGBF!VaJh;KVjD.#^F>Ja&;Bot ҼEl~h[jK4}Wwizm4 t/>njklN6ʫrtꡙ^XfkV$in7 _';6C]{/P57D1鱯jX&k)3.B,.ڏ'~Ao*j˘#!>JCLI21lM6yfgG幒}+2Sϰe2SY ȫ%û?yn 2!YXH^|=Ap >҇qceZw|̮gV1C+0 *mng.HpHϰ`ӧ :E#~pp ͽW$2\%斌x(||?r"'efnу`ל&8ۜLHWմ[Vg֥`1hF1&=~0D7ORK|KD&W$g`b0u$@ȅc#w3QSzݐ+ex@*jK6\wUȯю}T6< q{~2u?0dC`\iV>2hgġeԣ%!U`q tqی]rzzyOSC4рx!]lh8 |3 멓|@.C*L >]9C2* :]ax&cCsw|Tr[6_^"W%yMcP807&Ռ(]h6Vb{Ҧ{%~K|ˍl7Fc`@1^ KHCE4endstream endobj 459 0 obj <> endobj 460 0 obj [ 571 564 502 430 437 430 520 440 300 492 547 686 472 426 600 545 534 433 554 577 588 704 655 452 590 834 547 524 562 1043 1043 1043 1043 319 319 373 373 642 804 802 796 762 832 762 740 794 767 275 331 780 470 780 472 458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 419 412 445 948 948 468 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 487 735 ] endobj 461 0 obj <> endobj 462 0 obj <>stream %!PS-AdobeFont-1.1: RMTMI 1.1 %%CreationDate: 1993 May 10 16:52:31 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. % MathTime is a trademark of The TeXplorators Corporation 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation. Hinting (c) 1992, 1993 Y&Y, Inc. (508) 371-3286. All Rights Reserved.) readonly def /FullName (RMTMI) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle -14.036 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /WKXQXI+RMTMI def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 59 /comma put dup 17 /eta put dup 13 /gamma put dup 62 /greater put dup 21 /lambda put dup 60 /less put dup 23 /nu put dup 46 /parenleft put dup 47 /parenright put dup 58 /period put dup 30 /phi put dup 25 /pi put dup 32 /psi put dup 26 /rho put dup 27 /sigma put dup 61 /slash put dup 28 /tau put dup 18 /theta put dup 118 /v put dup 119 /w put dup 24 /xi put readonly def /FontBBox{0 -213 987 680}readonly def currentdict end currentfile eexec oc;j~EЪ+`U+1;[ihHlgtR@nk{#Y~gJ[. DI~ْ+%hapYz;3NO_O:Vп}KBhIϮԬ";eiwzVcW;I0a1]j"4[{ErGT1QeG0 Vw ߚOҎN'·4b>T(4^mѨnV8Bo8cpWTC 6j'-б^3;ZSd_ v9(+2Op?.BXsޝo!.Y([J$~8g@/Y.Y+S$C9S= iYRu |íPq.`1)KB/к!xYJK8,2(ŝ]#BEQw5,Ge2u fPQ6PnhH~l 棉l|6Ҿj;D鿂 "zGN8fYC8#SfMr =XZ2MIHv@}`6)ta}Y7Ϳ47_75Ww ^6u$; ӕcYfg_2ƨ4}ȱG}THl=YUX 3y-kHj7έD,3>(=?z#®2+)翱ِ2ٰԁ۠>>R̲ёK*ߟc5gRqUWIM FMx**&!Q@Wof&.4FQZ~a >-< n~bPEV~.u❓Fn&-҆t1~ > ;yJ9&eIyM.NkϘbyø279^rYdAm7tswaP鋁S''j XI~{iO )6IKyPK7M@ÅPc2VEX< =]Hi~XM# P9ȊF;i)`P]'j 'n7pZ)F8UIR0Npr (τR ȱ@Ј}Y!GRɏK:߯mI=ԿQɌ,K JPii}1y+} -F H$Ȩa_/~/A ' u -b,*Jt<]!e=("<E zc)N-BșɏM(D( b2U͌A3߂hnu1M{|p*O))Ø&| p.kI{=| DT65P0~Y]il%c9ךW߽ p$zo=T/ EHmÑ j+Ҩ_qv0txB4e  wCǷ Z[=SqKG4UҪZ/zZ'[u<%9\z;=(.;`-?7DU0 >kL"WwOlRϽVaܥҳ 9W?'břy*k\r*-i ]|\m_^d=]ϴ STرAζ ҧ\n1U{LJXX~\U7 iH1;=YRk,ޔmn_;oT2[S7 ڛקJ/lb]UKE bxF6a >Z"P'] +) MS&6tkϓE:pouy(V#(8\&\]+&Y`RbZakg\( ;+#r,CٵxLU.6VSBޡ xc(~]4-`z5G C)+8PN7v >*l0y/Gc@53,ӕh#*T h-'*VxW%`[E)X/ˡ ٚ3s<3 íN*TRoȤ5=Bܶ.R(wHc2sǽ2;vͨA)iCnQΕEWܦNC -3 nޡG#m7f M;s$8N׉gW{4R j5z/ÖD$%Dv\MB?% TxZ2h֎m%բ7Qj¤ _Ό ~RS4ҫb P0S`#lADNpO~Mc'k2zCR ]7[B31ҪqgK@(#,*RI›qVm<]=jyiH牒:Z' oaqOceQ evQ(çq- O^vR཯YHD[G!!Xr;CcvV$e"&b'7Fq3,ۦq$0 ܎K/W"ծGmexp*{tlJl_W޻x &.(+C6Īae[=; `u+QS9H/lSSco$Bى]Ll?;ՙLlUX"C{D<^qMZЖX̧CBqɴd]T T5@"|vE̜G\;} 8^mØ=dx%,gnc46'cݳU]ו`UH[\#KRNut38dޟAT2<#%4d5̏~;:q>NuӺpQ ΠS?.ͬ 'o@M5Ϝ@PrԃF=rCy&'CU,k<*+cy aߨ!#M׈/(^UւYcn)}oNoB@QQ„Lj0QI "CHv߸9x)?k sX-kDW.xAwʓKC c-eǧcݕt͗ql|a;7|ai6E2\:0ܸ?rx0S/BnZ E$֙6.ߡJW ([WfeR :Nt6W`:94WI^ap}%ϽSTs| %md}!9%97#͉*9t)$p- O4.!${Չ yy`J_2a33Ӡ.@=sfnnAgҁ@l3d ?/U*(ݠ$ ! ELᔙۂ+`\R@Lc@ r_xcP;:a?2DiO'I۴*hoD= 'D*j\YHR:DI:0@R<1k3cORGN<̻l/!܊4T:1(B2<`IeӓU AiԳ mNycl I*lQU\pf_;uos8dÀ}`y@E㡷άo"VLNq{lP -N)*Vob@WDӣ?֎`Mp\%cF_9K+^I%$vÁ!q)s+IwŇ)QQNv$ɂXI@_{ؑ8E,Tg)E\`idaC$ZpVg'展9Y\ۇL6M=h@ʯ{P:t ؚhgJ2Yf{z@h4 n<.1dXݼĻ.p}7,{1֒ t] rݧA dL%l>TT~ے)! 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F{ {Ϋ)xUfXo|ᝉ= 4ri7zTToPb8Fחy`g|'g qFu37haV߿&ϖYo R\vriۯsgB4Uظr ja #tй@O_uM_']@ |o[BQq E>xoD7QV 7T|FLN@t*c% R/Ź +u5xvV+Ev h5twO*1Х3WB*Mi?Kkcn$XG/࿶.t@+6)ENk 2t 9k̋u /g`ʹܲհլT&GhѸM/ڳƮy0p ѾPՌyy-no||Y8K}l;@wiuJl.#X/s|(x2D3Z%/_Vr7G>6s3!jՙd6ż u4󷒡%{4w};~)aŭN/z3#rH`DGd4*^gήQ.gY%lav;3%;yb eT^vms!5\\ZIU懹>2hcdO9}b(nq-m5N~w:1nhT*{j% 8OтS;& ?gB./[09!G`mtƺ@mo(<9M{fJp 8PnZm>Ēa٨䧙pjLmv)RCX\dADS7tH=1Sބ@`e2T@Cs3[ՄT Î G]_6y$pS-ϪsasCYs>岢%טJg Ekv4tI2=IY@:<~.I]_rNBw(FC>fC!#h>27c,mU)'{/yFr dV=Uk:/YNLwqF>f$=[m(A;NInq93'N)?"GuQ0N~+~Dn/+n\-ŇY%eCV 'uρz߾1tH"u鵽O1Lr_T3(3PcO)x֍P:B?+KQi$iCsصU+n30VkVyMƭ+ɥ96%~MOLsz<%8#R93AM%! ^ 04ȼVj%_ޕ, 6kR۞Vלֲw0߷Ԯ-(j]Gs8_H- `5)pQl淩LLf/O73$<ǻ%l Wv]Iz·%N%}rt1x*1\p7cֳBL̲θNuEOcI\99ى4ſ<̟'$j}vw$Q_+4`tG7R4R[Lʋ@EPFbt2]AW~6b|DfP>L.TJ䲳i0o\`*Hjs-E,ȯI^AGQJ=cتpյH"6In}ͳ#\޶Xi3TR'.jKG7ip5ڞ7wxA&IT27o*tiE0>quzTOeS7T0vv-B.v#}#IhH#9`XSt]6kӵsv_T┺a 2ISy3{o N=_Dɵ nNdP{xG[>&~ {Uڊ^-|69A玏MdءC1L*OE*^| 6>0ѤP&Q7Q|eA?0Iup޻oLmC)12Y ު)%)ݟ"ܳU,I Bdݓ/`^, L~Qkj&oS5 MKNѝIODzS’GZ X+`:[: o&鷠C̓cX/߫SuDPq(eyK'JH^‰OƲixp!>Qau:u*J02>[9~49G MO>tKdݩoQk/S!2(^'|Ns ^Bp?)1~L7k0 0^Ko铬疀 -IZ5l)gJ w):7-_Eve::wBur[bk"{4v¢6kq\'& 2vnN-޻""LDoCQ2ߏy!<8&}e(yIxe&Q%oX ߐ+Α]ʡ4hu}kn S"#ROA۰T8"( &7i=Fn$@ 1u` ٱ1%uT2Hi3*7,PM6LFCux.:C&1eR:ķMEv-%qjo ~e2C#O}`,#1ypqx޴91z3;ed ٺҟO>Z{Ӭ> GKb·E+s>9aL Qi:4-g,ސnq8GP+ѲRSYь܏V{xgTPwHA)CM(}" JI!YҋUScw@p{BOYE{D6Mk-*Ʌzfz*XW2ΦNΒ6rBsXhuOh~#EM83ek ^ v>8P Γg8닽aWrgC4u ŮQ`)D2A4玷ibxDm=;^Օ؀N@"|WPte<.C;~0Te(pdsضeW tm!P6(N.rv4Pyٙ{6삼(1%OJɀ8 *=AFkz˰A^WX(~x;IhmＧ&2 TI9rz^\hohS2A&m9ry*'B]tH):ZrrWR`G 'E4 )Pendstream endobj 467 0 obj <> endobj 468 0 obj [ 780 278 784 521 780 556 780 780 800 800 800 800 800 1000 500 500 780 780 780 780 754 754 754 754 780 780 780 780 984 984 754 754 1099 1099 616 616 1043 985 985 780 1043 1043 704 704 1043 985 985 762 270 1021 629 629 784 784 1 1 556 519 722 556 733 635 780 780 634 425 452 780 780 451 536 536 780 357 333 333 333 333 333 333 333 333 347 728 333 333 275 277 700 776 776 668 668 668 700 700 662 662 444 444 444 444 370 370 367 367 286 ] endobj 469 0 obj <> endobj 470 0 obj <>stream %!PS-AdobeFont-1.1: MTSYN 1.000 %%CreationDate: 1996 Aug 26 20:27:17 % Copyright (c) 1996 Michael Spivak. % Hinting Copyright (c) 1996 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.000) readonly def /Notice (Copyright (c) 1992-1996 Michael Spivak. 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[(transform\051.)-311(F)15(or)-311(e)15(xampl)1(e,)-311(let)-311(us)-310(state)-311(the)-310(solution)-311(of)-310(the)-311(tw)10(o-sided)-311(e)15(xit)-310(problem)-311(for)-310(completely)]TJ ET 1 0 0 1 45.354 464.587 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -464.587 cm BT /F117 9.9626 Tf 45.354 452.632 Td [(asymmetric)-347(stable)-346(processes.)-347(In)-347(that)-346(case)-347(we)-346(tak)10(e)]TJ/F126 9.9626 Tf 206.524 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F124 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)]TJ/F123 9.9626 Tf 6.213 0 Td [(x)]TJ/F121 9.9626 Tf 9.859 0 Td [(2)]TJ/F34 9.9626 Tf 10.815 0 Td [(R)]TJ/F117 9.9626 Tf 7.196 0 Td [(,)-347(to)-346(be)-347(a)-346(spectrally)-347(positi)25(v)15(e)]TJ ET 1 0 0 1 45.354 452.632 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -452.632 cm BT /F117 9.9626 Tf 45.354 440.677 Td [(L)]TJ 6.64 0.049 Td [(\264)]TJ -0.553 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9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F117 9.9626 Tf 11.733 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-72(.\013)]TJ/F121 9.9626 Tf 18.712 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ ET q 1 0 0 1 209.919 403.803 cm []0 d 0 J 0.458 w 0 0 m 56.26 0 l S Q BT /F126 9.9626 Tf 234.562 394.239 Td [(\031)]TJ/F151 9.9626 Tf 34.473 21.061 Td [(\022)]TJ/F123 9.9626 Tf 7.89 -7.004 Td [(a)]TJ/F121 9.9626 Tf 7.674 0 Td [(\000)]TJ/F123 9.9626 Tf 10.253 0 Td [(x)]TJ ET q 1 0 0 1 276.955 403.803 cm []0 d 0 J 0.458 w 0 0 m 23.207 0 l S Q BT /F123 9.9626 Tf 286.407 394.239 Td [(y)]TJ/F151 9.9626 Tf 14.951 21.061 Td [(\023)]TJ/F126 7.5716 Tf 6.725 -2.464 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 41.388 -4.54 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ ET q 1 0 0 1 325.755 403.803 cm []0 d 0 J 0.458 w 0 0 m 79.056 0 l S Q BT /F126 9.9626 Tf 325.755 394.239 Td [(.)]TJ/F123 9.9626 Tf 4.353 0 Td [(y)]TJ/F121 9.9626 Tf 7.156 0 Td [(C)]TJ/F123 9.9626 Tf 9.955 0 Td [(a)]TJ/F126 9.9626 Tf 5.459 0 Td [(/.)]TJ/F123 9.9626 Tf 8.07 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F123 9.9626 Tf 9.955 0 Td [(a)]TJ/F121 9.9626 Tf 7.673 0 Td [(\000)]TJ/F123 9.9626 Tf 10.254 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ 4.912 7.073 Td [(:)]TJ ET 1 0 0 1 45.354 401.312 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -401.312 cm BT /F117 9.9626 Tf 45.354 377.768 Td [(F)15(or)-198(the)-197(case)-198(of)-197(processes)-198(whose)-197(jumps)-198(are)-197(of)-198(a)-198(compound)-197(Poisson)-198(nature)-197(with)-198(e)15(xponential)-197(jumps,)]TJ ET 1 0 0 1 45.354 377.768 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -377.768 cm BT /F117 9.9626 Tf 45.354 365.813 Td [(the)-322(o)15(v)15(ershoot)-323(distrib)20(ution)-322(is)-323(ag)5(ain)-322(e)15(xponentially)-323(distrib)20(uted;)-322(see)-323(K)35(ou)-322(and)-322(W)80(ang)-323([)]TJ ET 1 0 0 1 375.284 365.813 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -375.284 -365.813 cm BT /F117 9.9626 Tf 375.284 365.813 Td [(18)]TJ ET 1 0 0 1 385.247 365.813 cm 0 g 0 G 1 0 0 1 -385.247 -365.813 cm BT /F117 9.9626 Tf 385.247 365.813 Td [(].)-323(See)-322(also)]TJ ET 1 0 0 1 45.354 365.813 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -365.813 cm BT /F117 9.9626 Tf 45.354 353.858 Td [(Le)25(wis)-223(and)-222(Mordecki)-223([)]TJ ET 1 0 0 1 132.546 353.858 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -132.546 -353.858 cm BT /F117 9.9626 Tf 132.546 353.858 Td [(21)]TJ ET 1 0 0 1 142.509 353.858 cm 0 g 0 G 1 0 0 1 -142.509 -353.858 cm BT /F117 9.9626 Tf 142.509 353.858 Td [(])-223(and)-222(Pistorius)-223([)]TJ ET 1 0 0 1 205.063 353.858 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -205.063 -353.858 cm BT /F117 9.9626 Tf 205.063 353.858 Td [(24)]TJ ET 1 0 0 1 215.025 353.858 cm 0 g 0 G 1 0 0 1 -215.025 -353.858 cm BT /F117 9.9626 Tf 215.025 353.858 Td [(])-223(for)-222(the)-223(more)-223(general)-222(case)-223(of)-223(a)-222(jump)-223(distrib)20(ution)-222(with)]TJ ET 1 0 0 1 45.354 353.858 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -353.858 cm BT /F117 9.9626 Tf 45.354 341.903 Td [(a)-299(rational)-300(F)15(ourier)-299(transform)-300(and)-299(for)-300(which)-299(the)-300(o)15(v)15(ershoot)-299(distrib)20(ution)-299(belongs)-300(to)-299(the)-300(same)-299(class)]TJ ET 1 0 0 1 45.354 341.903 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -341.903 cm BT /F117 9.9626 Tf 45.354 329.947 Td [(as)-250(the)-250(respecti)25(v)15(e)-250(jump)-250(distrib)20(ution)-250(of)-250(the)-250(underlying)-250(L)]TJ 216.9 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-250(process.)]TJ ET 1 0 0 1 45.354 329.947 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -329.947 cm BT /F117 9.9626 Tf 57.31 318.163 Td [(The)-250(e)15(xponential)-250(functional)-250(of)-250(a)-250(L)]TJ 134.041 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-250(process,)]TJ/F126 9.9626 Tf 51.735 0 Td [(\030)]TJ/F117 9.9626 Tf 5.34 0 Td [(,)-250(i.e.)]TJ ET 1 0 0 1 45.354 318.163 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -318.163 cm BT /F151 9.9626 Tf 69.265 308.108 Td [(Z)]TJ/F121 7.5716 Tf 9.823 -2.923 Td [(1)]TJ/F117 7.5716 Tf -4.563 -19.593 Td [(0)]TJ/F117 9.9626 Tf 14.452 8.957 Td [(e)15(xp)]TJ/F121 9.9626 Tf 14.237 0 Td [(f\000)]TJ/F126 9.9626 Tf 11.457 0 Td [(\030)]TJ/F123 7.5716 Tf 4.244 -1.495 Td [(s)]TJ/F121 9.9626 Tf 3.898 1.495 Td [(g)]TJ/F117 9.9626 Tf 5.346 0 Td [(d)]TJ/F123 9.9626 Tf 4.981 0 Td [(s)]TJ/F126 9.9626 Tf 4.274 0 Td [(;)]TJ ET 1 0 0 1 45.354 294.549 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -294.549 cm BT /F117 9.9626 Tf 45.354 271.406 Td [(also)-372(appears)-372(in)-372(v)25(arious)-373(aspects)-372(of)-372(probability)-372(theory)65(,)-372(such)-372(as:)-373(self-similar)-372(Mark)10(o)15(v)-372(processes,)]TJ ET 1 0 0 1 45.354 271.406 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -271.406 cm BT /F117 9.9626 Tf 45.354 259.451 Td [(random)-525(processes)-524(in)-525(random)-524(en)40(vironment,)-525(fragmentation)-525(processes,)-525(mathematical)-524(\002nance,)]TJ ET 1 0 0 1 45.354 259.451 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 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500.131 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -500.131 cm BT /F117 9.9626 Tf 39.797 488.176 Td [(e)15(xponential)-250(functional)-250(of)-250(L)]TJ 109.145 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy\226Lamperti)-250(processes.)]TJ ET 1 0 0 1 39.797 488.176 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -488.176 cm BT /F124 9.9626 Tf 39.797 465.368 Td [(2.)-500(Pr)18(eliminaries)-250(on)-250(L)]TJ 92.527 0.12 Td [(\264)]TJ -0.553 -0.12 Td [(evy\226Lamperti)-250(pr)18(ocesses)]TJ ET 1 0 0 1 39.797 465.368 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -465.368 cm BT /F117 9.9626 Tf 51.752 442.725 Td [(Denote)-277(by)]TJ/F160 9.9626 Tf 44.252 0 Td [(D)]TJ/F117 9.9626 Tf 10.721 0 Td [(the)-277(Sk)10(orokhod)-277(space)-277(of)]TJ/F34 9.9626 Tf 97.262 0 Td [(R)]TJ/F117 9.9626 Tf 7.195 0 Td [(-v)25(alued)-277(c)]TJ 37.364 0.05 Td [(\036)]TJ -0.553 -0.05 Td [(adl)]TJ 12.727 0.05 Td [(\036)]TJ -0.553 -0.05 Td [(ag)-277(paths)-277(and)-277(by)]TJ/F123 9.9626 Tf 66.587 0 Td [(X)]TJ/F117 9.9626 Tf 9.862 0 Td [(the)-277(canonical)-277(process)]TJ ET 1 0 0 1 39.797 442.725 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -442.725 cm BT /F117 9.9626 Tf 39.797 430.77 Td [(of)-317(the)-317(coordinates)-318(on)]TJ/F160 9.9626 Tf 89.005 0 Td [(D)]TJ/F117 9.9626 Tf 7.962 0 Td [(.)-318(Positi)25(v)15(e)-317(\050)]TJ/F34 9.9626 Tf 43.844 0 Td [(R)]TJ/F121 7.5716 Tf 7.195 -1.494 Td [(C)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(-v)25(alued\051,)-317(self-similar)-317(Mark)10(o)15(v)-318(processes)]TJ/F126 9.9626 Tf 162.927 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)]TJ/F123 9.9626 Tf 5.921 0 Td [(x)]TJ/F126 9.9626 Tf 9.318 0 Td [(>)]TJ/F117 9.9626 Tf 11.778 0 Td [(0,)]TJ ET 1 0 0 1 39.797 430.77 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -430.77 cm BT /F117 9.9626 Tf 39.797 418.815 Td [(are)-284(strong)-284(Mark)10(o)15(v)-284(processes)-284(with)-284(paths)-284(in)]TJ/F160 9.9626 Tf 172.845 0 Td [(D)]TJ/F117 9.9626 Tf 7.962 0 Td [(,)-284(which)-284(ful\002ll)-284(a)-284(scaling)-284(property)65(,)-284(i.e.)-284(there)-285(e)15(xists)-284(a)]TJ ET 1 0 0 1 39.797 418.815 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -418.815 cm BT /F117 9.9626 Tf 39.797 406.86 Td [(constant)]TJ/F126 9.9626 Tf 35.696 0 Td [(\013)-318(>)]TJ/F117 9.9626 Tf 19.392 0 Td [(0)-250(such)-250(that)-250(for)-250(an)15(y)]TJ/F123 9.9626 Tf 76.493 0 Td [(b)]TJ/F126 9.9626 Tf 7.948 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0:)]TJ ET 1 0 0 1 39.797 406.86 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -406.86 cm BT /F123 9.9626 Tf 63.707 388.014 Td [(The)-250(law)-250(of)]TJ/F126 9.9626 Tf 46.017 0 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(b)-97(X)]TJ/F123 7.5716 Tf 12.752 -2.001 Td [(b)]TJ/F121 5.9776 Tf 3.938 2.189 Td [(\000)]TJ/F126 5.9776 Tf 4.662 0 Td [(\013)]TJ/F123 7.5716 Tf 4.15 -2.189 Td [(t)]TJ/F126 9.9626 Tf 3.285 2.001 Td [(;)]TJ/F123 9.9626 Tf 6.618 0 Td [(t)]TJ/F121 9.9626 Tf 6.434 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F123 9.9626 Tf 6.207 0 Td [(under)]TJ/F34 9.9626 Tf 25.963 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.494 Td [(x)]TJ/F123 9.9626 Tf 7.025 1.494 Td [(is)]TJ/F34 9.9626 Tf 9.135 0 Td [(P)]TJ/F123 7.5716 Tf 6.089 -1.494 Td [(b)-47(x)]TJ/F126 9.9626 Tf 8.675 1.494 Td [(:)]TJ/F117 9.9626 Tf 163.349 0 Td [(\0502.1\051)]TJ ET 1 0 0 1 39.797 388.014 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -388.014 cm BT /F117 9.9626 Tf 39.797 369.169 Td [(W)80(e)-232(shall)-232(refer)-232(to)-232(these)-232(processes)-232(as)-232(pssMp.)-233(According)-232(to)-232(Lamperti)-232([)]TJ ET 1 0 0 1 309.283 369.169 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -309.283 -369.169 cm BT /F117 9.9626 Tf 309.283 369.169 Td [(20)]TJ ET 1 0 0 1 319.245 369.169 cm 0 g 0 G 1 0 0 1 -319.245 -369.169 cm BT /F117 9.9626 Tf 319.245 369.169 Td [(],)-232(an)15(y)-232(pssMp)-232(up)-232(to)-232(its)-232(\002rst)]TJ ET 1 0 0 1 39.797 369.169 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -369.169 cm BT /F117 9.9626 Tf 39.797 357.213 Td [(hitting)-321(time)-322(of)-321(0)-322(may)-321(be)-321(e)15(xpressed)-322(as)-321(the)-322(e)15(xponential)-321(of)-322(a)-321(L)]TJ 247.307 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-321(process,)-322(time)-321(changed)-322(by)-321(the)]TJ ET 1 0 0 1 39.797 357.213 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -357.213 cm BT /F117 9.9626 Tf 39.797 345.258 Td [(in)40(v)15(erse)-290(of)-291(its)-290(e)15(xponential)-291(functional.)-290(More)-291(formally)65(,)-290(let)]TJ/F126 9.9626 Tf 226.009 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(/)]TJ/F117 9.9626 Tf 6.61 0 Td [(be)-290(a)-291(pssMp)-290(with)-291(inde)15(x)]TJ/F126 9.9626 Tf 94.567 0 Td [(\013)-393(>)]TJ/F117 9.9626 Tf 20.885 0 Td [(0,)]TJ ET 1 0 0 1 39.797 345.258 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -345.258 cm BT /F117 9.9626 Tf 39.797 333.303 Td [(starting)-250(from)]TJ/F123 9.9626 Tf 54.505 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0,)-250(set)]TJ ET 1 0 0 1 39.797 333.303 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -333.303 cm BT /F123 9.9626 Tf 64.215 314.457 Td [(S)]TJ/F121 9.9626 Tf 8.197 0 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F121 9.9626 Tf 11.069 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F126 9.9626 Tf 6.433 0 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0)]TJ/F121 9.9626 Tf 7.748 0 Td [(V)]TJ/F123 9.9626 Tf 6.274 0 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.494 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F121 9.9626 Tf 4.981 0 Td [(g)]TJ ET 1 0 0 1 39.797 314.457 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -314.457 cm BT /F117 9.9626 Tf 39.797 295.612 Td [(and)-250(write)-250(the)-250(canonical)-250(process)]TJ/F123 9.9626 Tf 128.307 0 Td [(X)]TJ/F117 9.9626 Tf 9.594 0 Td [(in)-250(the)-250(follo)25(wing)-250(form:)]TJ ET 1 0 0 1 39.797 295.612 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -295.612 cm BT /F123 9.9626 Tf 64.474 275.108 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.495 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.495 Td [(D)]TJ/F123 9.9626 Tf 10.807 0 Td [(x)]TJ/F117 9.9626 Tf 6.97 0 Td [(e)15(xp)]TJ/F151 9.9626 Tf 15.897 8.009 Td [(\010)]TJ/F126 9.9626 Tf 4.723 -8.009 Td [(\030)]TJ/F126 7.5716 Tf 4.244 -2.001 Td [(\034)-120(.)]TJ/F123 7.5716 Tf 7.011 0 Td [(t)-117(x)]TJ/F121 5.9776 Tf 7.026 2.188 Td [(\000)]TJ/F126 5.9776 Tf 4.663 0 Td [(\013)]TJ/F126 7.5716 Tf 4.15 -2.188 Td [(/)]TJ/F151 9.9626 Tf 3.323 10.011 Td [(\011)]TJ/F117 9.9626 Tf 16.345 -8.01 Td [(0)]TJ/F121 9.9626 Tf 7.749 0 Td [(\024)]TJ/F123 9.9626 Tf 10.279 0 Td [(t)]TJ/F126 9.9626 Tf 6.433 0 Td [(<)]TJ/F123 9.9626 Tf 11.047 0 Td [(S)]TJ/F126 9.9626 Tf 5.429 0 Td [(;)]TJ/F117 9.9626 Tf 199.847 0 Td [(\0502.2\051)]TJ ET 1 0 0 1 39.797 275.108 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -275.108 cm BT /F117 9.9626 Tf 39.797 256.262 Td [(where)-250(for)]TJ/F123 9.9626 Tf 40.936 0 Td [(t)]TJ/F126 9.9626 Tf 6.434 0 Td [(<)]TJ/F123 9.9626 Tf 11.046 0 Td [(S)]TJ/F117 9.9626 Tf 5.43 0 Td [(,)]TJ ET 1 0 0 1 39.797 256.262 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -256.262 cm BT /F126 9.9626 Tf 63.707 232.525 Td [(\034)-120(.)]TJ/F123 9.9626 Tf 9.226 0 Td [(t)]TJ/F126 9.9626 Tf 3.666 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F151 9.9626 Tf 12.729 13.987 Td [(\032)]TJ/F123 9.9626 Tf 6.157 -13.987 Td [(s)]TJ/F121 9.9626 Tf 7.241 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F121 9.9626 Tf 7.748 0 Td [(V)]TJ/F151 9.9626 Tf 5.507 13.559 Td [(Z)]TJ/F123 7.5716 Tf 9.824 -2.923 Td [(s)]TJ/F117 7.5716 Tf -4.563 -19.593 Td [(0)]TJ/F117 9.9626 Tf 10.121 8.957 Td [(e)15(xp)]TJ/F121 9.9626 Tf 15.897 0.114 Td [(f)]TJ/F126 9.9626 Tf 3.686 -0.114 Td [(\013)-40(\030)]TJ/F123 7.5716 Tf 10.331 -1.495 Td [(u)]TJ/F121 9.9626 Tf 4.685 1.609 Td [(g)]TJ/F117 9.9626 Tf 5.347 -0.114 Td [(d)]TJ/F123 9.9626 Tf 4.981 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(\025)]TJ/F123 9.9626 Tf 10.279 0 Td [(t)]TJ/F151 9.9626 Tf 3.666 13.987 Td [(\033)]TJ/F126 9.9626 Tf 7.818 -13.987 Td [(:)]TJ ET 1 0 0 1 39.797 232.525 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -232.525 cm BT /F117 9.9626 Tf 39.797 208.31 Td [(Then)-256(under)]TJ/F34 9.9626 Tf 48.255 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F117 9.9626 Tf 4.534 1.494 Td [(,)]TJ/F126 9.9626 Tf 5.039 0 Td [(\030)]TJ/F121 9.9626 Tf 8.215 0 Td [(D)]TJ/F126 9.9626 Tf 10.646 0 Td [(.\030)]TJ/F123 7.5716 Tf 7.96 -1.494 Td [(t)]TJ/F126 9.9626 Tf 3.285 1.494 Td [(;)]TJ/F123 9.9626 Tf 7.833 0 Td [(t)]TJ/F121 9.9626 Tf 6.541 0 Td [(\025)]TJ/F117 9.9626 Tf 10.387 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 6.265 0 Td [(is)-256(a)-256(L)]TJ 22.806 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-256(process)-256(started)-255(from)-256(0)-256(whose)-256(la)15(w)-256(does)-256(not)-255(depend)-256(on)]TJ ET 1 0 0 1 39.797 208.31 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -208.31 cm BT /F123 9.9626 Tf 40.066 196.355 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)-250(and)-250(such)-250(that:)]TJ ET 1 0 0 1 39.797 196.355 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -16.686 cm 0 g 0 G 1 0 0 1 -39.797 -179.669 cm BT /F117 9.9626 Tf 45.336 179.669 Td [(\050i\051)]TJ ET 1 0 0 1 54.74 179.669 cm 0 g 0 G 1 0 0 1 -54.74 -179.669 cm BT /F117 9.9626 Tf 58.725 179.669 Td [(if)]TJ/F34 9.9626 Tf 8.578 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F121 9.9626 Tf 8.197 0 Td [(D)-278(C1)]TJ/F126 9.9626 Tf 28.481 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(1,)-250(then)]TJ/F126 9.9626 Tf 29.609 0 Td [(\030)]TJ/F117 9.9626 Tf 7.831 0 Td [(has)-250(an)-250(in\002nite)-250(lifetime)-250(and)-250(lim)-167(sup)]TJ/F123 7.5716 Tf 137.539 -2.536 Td [(t)]TJ/F121 7.5716 Tf 2.786 0 Td [(!C1)]TJ/F126 9.9626 Tf 24.116 2.536 Td [(\030)]TJ/F123 7.5716 Tf 4.244 -1.495 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.495 Td [(D)-278(C1)]TJ/F117 9.9626 Tf 28.481 0 Td [(,)]TJ/F34 9.9626 Tf 4.981 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.495 Td [(x)]TJ/F117 9.9626 Tf 4.534 1.495 Td [(-a.s.,)]TJ ET 1 0 0 1 39.797 179.669 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -11.872 cm 0 g 0 G 1 0 0 1 -39.797 -167.797 cm BT /F117 9.9626 Tf 42.566 167.797 Td [(\050ii\051)]TJ ET 1 0 0 1 54.74 167.797 cm 0 g 0 G 1 0 0 1 -54.74 -167.797 cm BT /F117 9.9626 Tf 58.725 167.797 Td [(if)]TJ/F34 9.9626 Tf 9.014 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F126 9.9626 Tf 9.003 0 Td [(<)]TJ/F121 9.9626 Tf 11.345 0 Td [(C1)]TJ/F126 9.9626 Tf 17.943 0 Td [(;)]TJ/F123 9.9626 Tf 7.385 0 Td [(X)]TJ/F126 9.9626 Tf 7.382 0 Td [(.)]TJ/F123 9.9626 Tf 4.225 0 Td [(S)]TJ/F121 9.9626 Tf 5.429 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(/)]TJ/F121 9.9626 Tf 7.29 0 Td [(D)]TJ/F117 9.9626 Tf 11.344 0 Td [(0)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F121 9.9626 Tf 7.289 0 Td [(D)]TJ/F117 9.9626 Tf 11.345 0 Td [(1,)-294(then)]TJ/F126 9.9626 Tf 30.48 0 Td [(\030)]TJ/F117 9.9626 Tf 8.266 0 Td [(has)-294(an)-293(in\002nite)-294(lifetime)-294(and)-293(lim)]TJ/F123 7.5716 Tf 124.217 -1.494 Td [(t)]TJ/F121 7.5716 Tf 2.787 0 Td [(!1)]TJ/F126 9.9626 Tf 18.21 1.494 Td [(\030)]TJ/F123 7.5716 Tf 4.244 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.858 1.494 Td [(D)-359(\0001)]TJ/F117 9.9626 Tf 29.287 0 Td [(,)]TJ ET 1 0 0 1 39.797 167.797 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -167.797 cm BT /F34 9.9626 Tf 58.725 155.842 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F117 9.9626 Tf 4.534 1.494 Td [(-a.s.,)]TJ ET 1 0 0 1 39.797 155.842 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -11.872 cm 0 g 0 G 1 0 0 1 -39.797 -143.97 cm BT /F117 9.9626 Tf 39.797 143.97 Td [(\050iii\051)]TJ ET 1 0 0 1 54.74 143.97 cm 0 g 0 G 1 0 0 1 -54.74 -143.97 cm BT /F117 9.9626 Tf 58.725 143.97 Td [(if)]TJ/F34 9.9626 Tf 10.244 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.533 1.494 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F126 9.9626 Tf 11.282 0 Td [(<)]TJ/F121 9.9626 Tf 13.623 0 Td [(C1)]TJ/F126 9.9626 Tf 17.942 0 Td [(;)]TJ/F123 9.9626 Tf 7.386 0 Td [(X)]TJ/F126 9.9626 Tf 7.382 0 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F121 9.9626 Tf 5.43 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(/)-587(>)]TJ/F117 9.9626 Tf 23.191 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 9.9626 Tf 9.568 0 Td [(D)]TJ/F117 9.9626 Tf 13.623 0 Td [(1,)-417(then)]TJ/F126 9.9626 Tf 32.942 0 Td [(\030)]TJ/F117 9.9626 Tf 9.496 0 Td [(is)-417(killed)-417(at)-418(an)-417(independent)-417(e)15(xponentially)]TJ ET 1 0 0 1 39.797 143.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -143.97 cm BT /F117 9.9626 Tf 58.725 132.015 Td [(distrib)20(uted)-250(random)-250(time)-250(with)-250(parameter)]TJ/F126 9.9626 Tf 160.566 0 Td [(\025)-278(>)]TJ/F117 9.9626 Tf 18.755 0 Td [(0.)]TJ ET 1 0 0 1 39.797 132.015 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -132.015 cm BT /F117 9.9626 Tf 51.752 115.183 Td [(As)-398(mentioned)-399(in)-398([)]TJ ET 1 0 0 1 127.86 115.183 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -127.86 -115.183 cm BT /F117 9.9626 Tf 127.86 115.183 Td [(20)]TJ ET 1 0 0 1 137.823 115.183 cm 0 g 0 G 1 0 0 1 -137.823 -115.183 cm BT /F117 9.9626 Tf 137.823 115.183 Td [(],)-399(the)-398(probabilities)]TJ/F34 9.9626 Tf 79.706 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F121 9.9626 Tf 10.936 0 Td [(D)-553(C1)]TJ/F126 9.9626 Tf 31.22 0 Td [(/;)]TJ/F34 9.9626 Tf 8.675 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F126 9.9626 Tf 10.936 0 Td [(<)]TJ/F121 9.9626 Tf 13.278 0 Td [(C1)]TJ/F126 9.9626 Tf 17.942 0 Td [(;)]TJ/F123 9.9626 Tf 7.386 0 Td [(X)]TJ/F126 9.9626 Tf 7.382 0 Td [(.)]TJ/F123 9.9626 Tf 4.224 0 Td [(S)]TJ/F121 9.9626 Tf 5.43 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(/)]TJ/F121 9.9626 Tf 9.223 0 Td [(D)]TJ/F117 9.9626 Tf 13.277 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 7.686 0 Td [(and)]TJ ET 1 0 0 1 39.797 115.183 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -115.183 cm BT /F34 9.9626 Tf 39.797 103.228 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.533 1.495 Td [(.)]TJ/F123 9.9626 Tf 4.225 0 Td [(S)]TJ/F126 9.9626 Tf 9.61 0 Td [(<)]TJ/F121 9.9626 Tf 11.951 0 Td [(C1)]TJ/F126 9.9626 Tf 17.943 0 Td [(;)]TJ/F123 9.9626 Tf 7.385 0 Td [(X)]TJ/F126 9.9626 Tf 7.382 0 Td [(.)]TJ/F123 9.9626 Tf 4.225 0 Td [(S)]TJ/F121 9.9626 Tf 5.429 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(/)-420(>)]TJ/F117 9.9626 Tf 19.848 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 6.97 0 Td 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5.459 4.114 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -4.114 Td [(\025)]TJ/F121 9.9626 Tf 7.663 0 Td [(C)]TJ/F151 9.9626 Tf 9.985 13.559 Td [(Z)]TJ/F35 7.9701 Tf 5.26 -22.516 Td [(R)]TJ/F121 9.9626 Tf 6.255 8.957 Td [(T)]TJ/F117 9.9626 Tf 3.317 0 Td [(e)]TJ/F117 7.5716 Tf 4.424 4.114 Td [(i)]TJ/F126 7.5716 Tf 2.104 0 Td [(\025)]TJ/F123 7.5716 Tf 4.347 0 Td [(x)]TJ/F121 9.9626 Tf 6.747 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(i)]TJ/F126 9.9626 Tf 2.769 0 Td [(\025.)]TJ/F117 9.9626 Tf 9.166 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 4.114 Td [(x)]TJ/F121 9.9626 Tf 6.747 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F161 9.9626 Tf 3.717 0 Td [(1)]TJ/F121 7.5716 Tf 5.534 -1.498 Td [(fj)]TJ/F117 7.5716 Tf 4.967 0 Td [(e)]TJ/F123 5.9776 Tf 3.523 2.188 Td [(x)]TJ/F121 7.5716 Tf 3.685 -2.188 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(j)]TJ/F126 7.5716 Tf 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9.9626 Tf 6.934 -3.617 Td [(is)-250(a)-250(constant,)]TJ ET 1 0 0 1 45.354 413.248 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -413.248 cm BT /F126 9.9626 Tf 69.265 390.005 Td [(\031)]TJ/F121 7.5716 Tf 6.974 4.115 Td [(\003)]TJ/F126 9.9626 Tf 4.442 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.986 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 26.034 6.984 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(C)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(e)]TJ/F123 7.5716 Tf 4.628 3.617 Td [(x)]TJ ET q 1 0 0 1 108.194 392.496 cm []0 d 0 J 0.458 w 0 0 m 48.59 0 l S Q BT /F126 9.9626 Tf 108.194 382.849 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 2.879 Td [(x)]TJ/F121 9.9626 Tf 6.747 -2.879 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 2.879 Td [(\013)]TJ/F121 7.5716 Tf 4.627 0 Td [(C)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F161 9.9626 Tf 5.48 4.277 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.497 Td [(f)]TJ/F123 7.5716 Tf 3.006 0 Td [(x)]TJ/F126 7.5716 Tf 4.035 0 Td [(>)]TJ/F117 7.5716 Tf 5.906 0 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(g)]TJ/F121 9.9626 Tf 5.513 1.497 Td [(C)]TJ/F123 9.9626 Tf 25.481 6.984 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(e)]TJ/F123 7.5716 Tf 4.628 3.617 Td [(x)]TJ ET q 1 0 0 1 196.941 392.496 cm []0 d 0 J 0.458 w 0 0 m 48.59 0 l S Q BT /F126 9.9626 Tf 196.941 382.849 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.627 2.879 Td [(x)]TJ/F126 9.9626 Tf 4.534 -2.879 Td [(/)]TJ/F126 7.5716 Tf 3.716 2.879 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F161 9.9626 Tf 5.48 4.277 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.497 Td [(f)]TJ/F123 7.5716 Tf 3.005 0 Td [(x)]TJ/F126 7.5716 Tf 4.036 0 Td [(<)]TJ/F117 7.5716 Tf 5.906 0 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(g)]TJ/F126 9.9626 Tf 3.299 1.497 Td [(;)]TJ ET 1 0 0 1 45.354 390.005 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -390.005 cm BT /F117 9.9626 Tf 45.354 366.171 Td [(and)]TJ/F123 9.9626 Tf 17.038 0 Td [(c)]TJ/F121 7.5716 Tf 4.424 -1.495 Td [(\000)]TJ/F117 9.9626 Tf 6.404 1.495 Td [(,)]TJ/F123 9.9626 Tf 5.143 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.495 Td [(C)]TJ/F117 9.9626 Tf 9.056 1.495 Td [(are)-266(nonne)15(g)5(ati)25(v)15(e)-266(constants)-267(such)-266(that)]TJ/F123 9.9626 Tf 143.81 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.495 Td [(\000)]TJ/F121 9.9626 Tf 8.737 1.495 Td [(C)]TJ/F123 9.9626 Tf 10.105 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.495 Td [(C)]TJ/F126 9.9626 Tf 9.47 1.495 Td [(>)]TJ/F117 9.9626 Tf 10.837 0 Td [(0.)-266(Note)-267(that)-266(the)-266(L)]TJ 71.207 0.049 Td [(\264)]TJ -0.553 -0.049 Td [(evy)-266(measure)-266(of)]TJ/F126 9.9626 Tf 63.836 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ ET 1 0 0 1 45.354 366.171 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -366.171 cm BT /F117 9.9626 Tf 45.354 354.215 Td [(satis\002es)]TJ/F126 9.9626 Tf 34.421 0 Td [(\031)]TJ/F121 7.5716 Tf 6.974 3.617 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.617 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 7.186 0 Td [(D)]TJ/F117 9.9626 Tf 11.24 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 3.617 Td [(x)]TJ/F126 9.9626 Tf 4.534 -3.617 Td [(\027)-60(.)]TJ/F117 9.9626 Tf 9.016 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 3.617 Td [(x)]TJ/F121 9.9626 Tf 7.028 -3.617 Td [(\000)]TJ/F117 9.9626 Tf 10.266 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)-288(where)]TJ/F126 9.9626 Tf 32.569 0 Td [(\027)]TJ/F117 9.9626 Tf 8.17 0 Td [(is)-288(the)-288(density)-288(of)-288(the)-288(stable)-288(L)]TJ 115.175 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-288(measure)-288(with)-288(inde)15(x)]TJ/F126 9.9626 Tf 98.762 0 Td [(\013)]TJ ET 1 0 0 1 45.354 354.215 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -354.215 cm BT /F117 9.9626 Tf 45.354 342.26 Td [(and)-250(symmetry)-250(parameters)]TJ/F123 9.9626 Tf 105.414 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ/F117 9.9626 Tf 8.895 1.494 Td [(and)]TJ/F123 9.9626 Tf 16.877 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(C)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(.)]TJ ET 1 0 0 1 45.354 342.26 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -342.26 cm BT /F117 9.9626 Tf 57.31 330.349 Td [(The)-361(second)-360(class)-361(is)-361(that)-361(of)-360(stable)-361(processes)-361(conditioned)-361(to)-360(stay)-361(positi)25(v)15(e.)-362(\050See)-360(for)-361(instance)]TJ ET 1 0 0 1 45.354 330.349 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -330.349 cm BT /F117 9.9626 Tf 45.354 318.394 Td [(in)-333([)]TJ ET 1 0 0 1 59.738 318.394 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -59.738 -318.394 cm BT /F117 9.9626 Tf 59.738 318.394 Td [(12)]TJ ET 1 0 0 1 69.701 318.394 cm 0 g 0 G 1 0 0 1 -69.701 -318.394 cm BT /F117 9.9626 Tf 69.701 318.394 Td [(])-333(for)-332(an)-333(o)15(v)15(ervie)25(w)-333(of)-333(such)-333(processes.\051)-333(Processes)-333(in)-332(this)-333(class)-333(are)-333(the)-332(result)-333(of)-333(a)-333(Doob)]TJ/F123 9.9626 Tf 349.402 0 Td [(h)]TJ/F117 9.9626 Tf 5.499 0 Td [(-)]TJ ET 1 0 0 1 45.354 318.394 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -318.394 cm BT /F117 9.9626 Tf 45.354 306.439 Td [(transforming)-291(stable)-291(processes)-291(killed)-291(on)-291(e)15(xiting)]TJ/F126 9.9626 Tf 190.467 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F121 9.9626 Tf 4.958 0 Td [(1)]TJ/F126 9.9626 Tf 10.172 0 Td [(/)]TJ/F117 9.9626 Tf 6.616 0 Td [(with)]TJ/F123 9.9626 Tf 20.663 0 Td [(h)]TJ/F126 9.9626 Tf 5.499 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 7.241 0 Td [(D)]TJ/F123 9.9626 Tf 11.564 0 Td [(x)]TJ/F126 7.5716 Tf 5.31 3.616 Td [(\013)40(\032)]TJ/F117 9.9626 Tf 12 -3.616 Td [(and)]TJ/F126 9.9626 Tf 17.285 0 Td [(\032)]TJ/F121 9.9626 Tf 9.552 0 Td [(D)]TJ/F124 9.9626 Tf 11.296 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(0)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F117 7.5716 Tf 6.805 -1.497 Td [(1)]TJ/F126 9.9626 Tf 7.808 1.497 Td [(<)]TJ/F117 9.9626 Tf 11.296 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(.)]TJ ET 1 0 0 1 45.354 306.439 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -306.439 cm BT /F117 9.9626 Tf 45.354 294.484 Td [(More)-207(precisely)65(,)]TJ/F123 9.9626 Tf 63.557 0 Td [(h)]TJ/F117 9.9626 Tf 7.56 0 Td [(is)-207(an)-206(in)40(v)25(ariant)-207(function)-207(for)-207(the)-207(kill)1(ed)-207(process)-207(mentioned)-207(abo)15(v)15(e,)]TJ/F126 9.9626 Tf 249.031 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.495 Td [(t)]TJ/F161 9.9626 Tf 3.284 1.495 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.495 Td [(f)]TJ/F123 7.5716 Tf 2.801 0 Td [(t)]TJ/F126 7.5716 Tf 2.787 0 Td [(<)]TJ/F123 7.5716 Tf 6.08 0 Td [(T)]TJ/F121 7.5716 Tf 5.353 0 Td [(g)]TJ/F126 9.9626 Tf 3.3 1.495 Td [(;)]TJ/F124 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.291 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)]TJ ET 1 0 0 1 45.354 294.484 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -294.484 cm BT /F117 9.9626 Tf 45.354 280.4 Td [(and)-250(the)-250(la)15(w)]TJ/F34 9.9626 Tf 48.269 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.104 Td [(")]TJ/F123 7.5716 Tf 0.205 -6.716 Td [(x)]TJ/F117 9.9626 Tf 7.448 1.612 Td [(de\002ned)-250(on)-250(each)]TJ/F126 9.9626 Tf 65.016 0 Td [(\033)]TJ/F117 9.9626 Tf 6.615 0 Td [(-\002eld)]TJ/F160 9.9626 Tf 23.522 0 Td [(F)]TJ/F123 7.5716 Tf 7.16 -1.495 Td [(t)]TJ/F117 9.9626 Tf 5.775 1.495 Td [(generated)-250(by)-250(the)-250(canonical)-250(process)-250(up)-250(to)-250(time)]TJ/F123 9.9626 Tf 184.268 0 Td [(t)]TJ/F117 9.9626 Tf 6.156 0 Td [(by)]TJ ET 1 0 0 1 45.354 280.4 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -280.4 cm BT /F117 9.9626 Tf 71.656 258.007 Td [(d)]TJ/F34 9.9626 Tf 4.981 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.104 Td [(")]TJ/F123 7.5716 Tf 0.205 -6.716 Td [(x)]TJ ET q 1 0 0 1 71.656 253.513 cm []0 d 0 J 0.458 w 0 0 m 16.232 0 l S Q BT /F117 9.9626 Tf 71.868 243.949 Td [(d)]TJ/F124 9.9626 Tf 4.982 0 Td [(P)]TJ/F123 7.5716 Tf 6.291 -1.494 Td [(x)]TJ/F151 9.9626 Tf 5.942 26.002 Td [(\014)]TJ 0 -5.977 Td [(\014)]TJ 0 -5.978 Td [(\014)]TJ 0 -5.977 Td [(\014)]TJ 0 -5.978 Td [(\014)]TJ/F164 7.9701 Tf 3.238 -6.356 Td [(F)]TJ/F123 5.9776 Tf 6.044 -1.136 Td [(t)]TJ/F121 9.9626 Tf 5.963 13.968 Td [(D)]TJ/F123 9.9626 Tf 12.501 6.984 Td [(X)]TJ/F126 7.5716 Tf 7.103 5.097 Td [(\013)40(\032)]TJ/F123 7.5716 Tf -0.298 -7.474 Td [(t)]TJ ET q 1 0 0 1 116.062 253.513 cm []0 d 0 J 0.458 w 0 0 m 16.97 0 l S Q BT /F123 9.9626 Tf 117.477 243.949 Td [(x)]TJ/F126 7.5716 Tf 5.31 2.879 Td [(\013)40(\032)]TJ/F161 9.9626 Tf 11.44 4.195 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.495 Td [(f)]TJ/F123 7.5716 Tf 2.802 0 Td [(t)]TJ/F126 7.5716 Tf 2.786 0 Td [(<)]TJ/F123 7.5716 Tf 6.08 0 Td [(T)]TJ/F121 7.5716 Tf 5.353 0 Td [(g)]TJ/F117 9.9626 Tf 252.048 1.495 Td [(\0502.5\051)]TJ ET 1 0 0 1 45.354 251.023 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -251.023 cm BT /F117 9.9626 Tf 45.354 222.378 Td [(is)-371(that)-372(of)-371(a)-372(pssMp)-371(which)-371(drifts)-372(to)25(w)10(ard)]TJ/F121 9.9626 Tf 163.18 0 Td [(C1)]TJ/F117 9.9626 Tf 21.643 0 Td [(\050in)-371(particular)-372(it)-371(satis\002es)-372(condition)-371(\050i\051\051.)-372(Then)-372(the)]TJ ET 1 0 0 1 45.354 222.378 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -222.378 cm BT /F117 9.9626 Tf 45.354 210.423 Td [(underlying)-250(L)]TJ 52.299 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-250(process,)-250(which)-250(will)-250(be)-250(denoted)-250(by)]TJ/F126 9.9626 Tf 154.948 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F117 9.9626 Tf 5.162 -3.617 Td [(,)-250(is)-250(such)-250(that)]TJ ET 1 0 0 1 45.354 210.423 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -210.423 cm BT /F117 9.9626 Tf 74.992 190.318 Td [(lim)]TJ/F123 7.5716 Tf -5.727 -6.177 Td [(t)]TJ/F121 7.5716 Tf 2.786 0 Td [(!C1)]TJ/F126 9.9626 Tf 23.618 6.177 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -1.096 -7.481 Td [(t)]TJ/F121 9.9626 Tf 9.026 2.376 Td [(D)-278(C1)]TJ/F126 9.9626 Tf 28.48 0 Td [(;)]TJ/F117 9.9626 Tf 14.921 0 Td [(a.s.,)]TJ ET 1 0 0 1 45.354 190.318 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -190.318 cm BT /F117 9.9626 Tf 45.354 167.818 Td [(and)-250(from)-250([)]TJ ET 1 0 0 1 87.406 167.818 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -87.406 -167.818 cm BT /F117 9.9626 Tf 87.406 167.818 Td [(10)]TJ ET 1 0 0 1 97.369 167.818 cm 0 g 0 G 1 0 0 1 -97.369 -167.818 cm BT /F117 9.9626 Tf 97.369 167.818 Td [(])-250(its)-250(characteristic)-250(e)15(xponent)-250(is)]TJ ET 1 0 0 1 45.354 167.818 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -167.818 cm BT /F40 9.9626 Tf 69.265 142.317 Td [(\010)]TJ/F121 7.5716 Tf 7.725 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.\025/)]TJ/F121 9.9626 Tf 15.649 0 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(i)]TJ/F123 9.9626 Tf 2.74 0 Td [(a)]TJ/F121 7.5716 Tf 5.459 4.114 Td [(")]TJ/F126 9.9626 Tf 5.163 -4.114 Td [(\025)]TJ/F121 9.9626 Tf 7.663 0 Td [(C)]TJ/F151 9.9626 Tf 9.985 13.559 Td [(Z)]TJ/F35 7.9701 Tf 5.26 -22.516 Td [(R)]TJ/F121 9.9626 Tf 6.254 8.957 Td [(T)]TJ/F117 9.9626 Tf 3.318 0 Td [(e)]TJ/F117 7.5716 Tf 4.423 4.114 Td [(i)]TJ/F126 7.5716 Tf 2.105 0 Td [(\025)]TJ/F123 7.5716 Tf 4.346 0 Td [(x)]TJ/F121 9.9626 Tf 6.748 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F123 9.9626 Tf 9.915 0 Td [(i)]TJ/F126 9.9626 Tf 3.736 0 Td [(\025.)]TJ/F117 9.9626 Tf 9.165 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 4.114 Td [(x)]TJ/F121 9.9626 Tf 6.748 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F161 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.498 Td [(fj)]TJ/F117 7.5716 Tf 4.967 0 Td [(e)]TJ/F123 5.9776 Tf 3.523 2.188 Td [(x)]TJ/F121 7.5716 Tf 3.684 -2.188 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(j)]TJ/F126 7.5716 Tf 2.165 0 Td [(<)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(g)]TJ/F121 9.9626 Tf 3.299 1.498 Td [(U)]TJ/F126 9.9626 Tf 3.318 0 Td [(\031)]TJ/F121 7.5716 Tf 6.974 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F117 9.9626 Tf 5.377 0 Td [(d)]TJ/F123 9.9626 Tf 5.25 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)-1167(\025)]TJ/F121 9.9626 Tf 23.138 0 Td [(2)]TJ/F34 9.9626 Tf 9.033 0 Td [(R)]TJ/F126 9.9626 Tf 7.196 0 Td [(;)]TJ/F117 9.9626 Tf 44.364 0 Td [(\0502.6\051)]TJ ET 1 0 0 1 45.354 142.317 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -142.317 cm BT /F117 9.9626 Tf 45.354 116.901 Td [(where)]TJ/F123 9.9626 Tf 26.8 0 Td [(a)]TJ/F121 7.5716 Tf 5.459 3.616 Td [(")]TJ/F117 9.9626 Tf 7.653 -3.616 Td [(is)-250(a)-250(real)-250(constant)-250(and)]TJ ET 1 0 0 1 45.354 116.901 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -116.901 cm BT /F126 9.9626 Tf 69.265 93.157 Td [(\031)]TJ/F121 7.5716 Tf 6.974 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 14.064 6.983 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(C)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.617 Td [(.\013)40(\032)]TJ/F121 7.5716 Tf 11.426 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F123 7.5716 Tf 3.028 0 Td [(x)]TJ ET q 1 0 0 1 108.913 95.647 cm []0 d 0 J 0.458 w 0 0 m 48.59 0 l S Q BT /F126 9.9626 Tf 108.913 86 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 2.88 Td [(x)]TJ/F121 9.9626 Tf 6.747 -2.88 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 2.88 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F161 9.9626 Tf 5.479 4.277 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.498 Td [(f)]TJ/F123 7.5716 Tf 3.006 0 Td [(x)]TJ/F126 7.5716 Tf 4.036 0 Td [(>)]TJ/F117 7.5716 Tf 5.905 0 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(g)]TJ/F121 9.9626 Tf 5.514 1.498 Td [(C)]TJ/F123 9.9626 Tf 13.51 6.983 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ/F117 9.9626 Tf 6.404 1.494 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.617 Td [(.\013)40(\032)]TJ/F121 7.5716 Tf 11.426 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F123 7.5716 Tf 3.028 0 Td [(x)]TJ ET q 1 0 0 1 197.66 95.647 cm []0 d 0 J 0.458 w 0 0 m 48.59 0 l S Q BT /F126 9.9626 Tf 197.66 86 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.628 2.88 Td [(x)]TJ/F126 9.9626 Tf 4.533 -2.88 Td [(/)]TJ/F126 7.5716 Tf 3.717 2.88 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F161 9.9626 Tf 5.479 4.277 Td [(1)]TJ/F121 7.5716 Tf 5.535 -1.498 Td [(f)]TJ/F123 7.5716 Tf 3.006 0 Td [(x)]TJ/F126 7.5716 Tf 4.035 0 Td [(<)]TJ/F117 7.5716 Tf 5.906 0 Td [(0)]TJ/F121 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375.973 Td [(Note)-217(that)-216(the)-217(constants)]TJ/F123 9.9626 Tf 92.168 0 Td [(a)]TJ/F121 7.5716 Tf 5.459 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(;)]TJ/F123 9.9626 Tf 4.928 0 Td [(a)]TJ/F121 7.5716 Tf 5.46 3.616 Td [(")]TJ/F117 9.9626 Tf 7.32 -3.616 Td [(and)]TJ/F123 9.9626 Tf 16.514 0 Td [(a)]TJ/F121 7.5716 Tf 5.46 3.616 Td [(#)]TJ/F117 9.9626 Tf 7.32 -3.616 Td [(are)-217(computed)-216(e)15(xplicitly)-217(in)-216([)]TJ ET 1 0 0 1 297.515 375.973 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -297.515 -375.973 cm BT /F117 9.9626 Tf 297.515 375.973 Td [(10)]TJ ET 1 0 0 1 307.478 375.973 cm 0 g 0 G 1 0 0 1 -307.478 -375.973 cm BT /F117 9.9626 Tf 307.478 375.973 Td [(])-217(in)-216(terms)-217(of)]TJ/F126 9.9626 Tf 50.136 0 Td [(\013;)-167(\032)-87(;)]TJ/F123 9.9626 Tf 21.901 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.495 Td [(\000)]TJ/F117 9.9626 Tf 8.562 1.495 Td [(and)]TJ/F123 9.9626 Tf 16.544 0 Td [(c)]TJ/F121 7.5716 Tf 4.424 -1.495 Td [(C)]TJ/F117 9.9626 Tf 6.404 1.495 Td [(.)]TJ ET 1 0 0 1 39.797 375.973 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -375.973 cm BT /F117 9.9626 Tf 39.797 364.018 Td [(Actually)-231(the)-232(process)]TJ/F126 9.9626 Tf 83.278 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 7.468 -3.616 Td [(corresponds)-231(to)]TJ/F126 9.9626 Tf 60.5 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F117 9.9626 Tf 7.468 -3.616 Td [(conditioned)-231(to)-232(drift)-231(to)25(w)10(ard)]TJ/F121 9.9626 Tf 108.487 0 Td [(\0001)]TJ/F117 9.9626 Tf 20.248 0 Td [(\050or)-231(equi)25(v)25(alently)]TJ/F126 9.9626 Tf 64.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F117 9.9626 Tf 7.467 -3.616 Td [(is)]TJ ET 1 0 0 1 39.797 364.018 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -364.018 cm BT /F126 9.9626 Tf 39.797 352.062 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(#)]TJ/F117 9.9626 Tf 7.499 -3.617 Td [(conditioned)-235(to)-234(drift)-235(to)]TJ/F121 9.9626 Tf 89.049 0 Td [(C1)]TJ/F117 9.9626 Tf 17.943 0 Td [(\051.)-235(W)80(e)-234(will)-235(sometime)-234(use)-235(this)-235(relationship)-234(which)-235(is)-234(stated)-235(in)-234(a)-235(more)]TJ ET 1 0 0 1 39.797 352.062 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -352.062 cm BT /F117 9.9626 Tf 39.797 340.107 Td [(formal)-293(w)10(ay)-293(in)-294(the)-293(ne)15(xt)-293(proposition.)-293(In)-294(what)-293(follo)25(ws,)]TJ/F123 9.9626 Tf 214.834 0 Td [(P)]TJ/F117 9.9626 Tf 9.825 0 Td [(will)-293(be)-293(a)-294(reference)-293(probability)-293(measure)]TJ ET 1 0 0 1 39.797 340.107 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -340.107 cm BT /F117 9.9626 Tf 39.797 328.152 Td [(on)]TJ/F160 9.9626 Tf 12.415 0 Td [(D)]TJ/F117 9.9626 Tf 10.414 0 Td [(under)-246(which)]TJ/F126 9.9626 Tf 51.938 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(;)-167(\030)]TJ/F121 7.5716 Tf 10.298 3.616 Td [(")]TJ/F117 9.9626 Tf 7.614 -3.616 Td [(and)]TJ/F126 9.9626 Tf 16.838 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 7.615 -3.616 Td [(are)-246(L)]TJ 21.256 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-246(processes)-246(whose)-246(respecti)25(v)15(e)-247(la)15(ws)-246(are)-246(described)-246(abo)15(v)15(e.)]TJ ET 1 0 0 1 39.797 328.152 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.607 cm 0 g 0 G 1 0 0 1 -35.812 -305.545 cm BT /F124 9.9626 Tf 39.797 305.545 Td [(Pr)18(oposition)-250(1.)]TJ ET 1 0 0 1 98.845 305.545 cm 0 g 0 G 1 0 0 1 -98.845 -305.545 cm BT /F123 9.9626 Tf 102.83 305.545 Td [(F)105(or)-250(e)15(very)-250(t)]TJ/F121 9.9626 Tf 46.732 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F123 9.9626 Tf 4.982 0 Td [(,)-250(and)-250(e)15(very)-250(bounded)-250(measur)15(able)-250(function)-469(f)-209(,)]TJ ET 1 0 0 1 39.797 305.545 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -305.545 cm BT /F123 9.9626 Tf 64.395 285.834 Td [(E)]TJ/F121 9.9626 Tf 6.983 0 Td [(T)]TJ/F123 9.9626 Tf 5.5 0 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(")]TJ/F123 7.5716 Tf -1.096 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)-278(D)]TJ/F123 9.9626 Tf 17.31 0 Td [(E)]TJ/F121 9.9626 Tf 6.984 0 Td [(T)]TJ/F117 9.9626 Tf 3.318 0 Td [(e)15(xp)]TJ/F126 9.9626 Tf 14.236 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(#)]TJ/F123 7.5716 Tf -1.095 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F123 9.9626 Tf 5.898 0 Td [(f)]TJ/F126 9.9626 Tf 4.851 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(#)]TJ/F123 7.5716 Tf -1.095 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)]TJ/F126 9.9626 Tf 3.317 0 Td [(:)]TJ ET 1 0 0 1 39.797 285.834 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -285.834 cm BT /F123 9.9626 Tf 39.797 265.69 Td [(In)-534(particular)111(,)-533(pr)45(ocesses)]TJ/F121 9.9626 Tf 104.328 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F123 9.9626 Tf 10.479 -3.616 Td [(and)]TJ/F126 9.9626 Tf 20.529 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F123 9.9626 Tf 10.478 -3.616 Td [(satisfy)-534(Cr)15(amer')40(s)-533(condition:)-604(E)]TJ/F126 9.9626 Tf 127.686 0 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(e)15(xp)]TJ/F121 9.9626 Tf 15.897 0 Td [(\000)]TJ/F126 9.9626 Tf 7.77 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F117 7.5716 Tf -1.095 -8.436 Td [(1)]TJ/F126 9.9626 Tf 6.258 3.331 Td [(/)]TJ/F121 9.9626 Tf 11.715 0 Td [(D)]TJ/F117 9.9626 Tf 15.771 0 Td [(1)]TJ/F123 9.9626 Tf 10.297 0 Td [(and)]TJ ET 1 0 0 1 39.797 265.69 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -265.69 cm BT /F123 9.9626 Tf 40.484 251.208 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)15(xp)]TJ/F126 9.9626 Tf 15.897 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(#)]TJ/F117 7.5716 Tf -1.096 -8.435 Td [(1)]TJ/F126 9.9626 Tf 6.258 3.33 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(1)]TJ/F123 9.9626 Tf 4.981 0 Td [(.)]TJ ET 1 0 0 1 39.797 251.208 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -21.981 cm 0 g 0 G 1 0 0 1 -35.812 -229.227 cm BT /F124 9.9626 Tf 39.797 229.227 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 65.75 229.227 cm 0 g 0 G 1 0 0 1 -65.75 -229.227 cm BT /F117 9.9626 Tf 69.735 229.227 Td [(Let)]TJ/F123 9.9626 Tf 17.868 0 Td [(f)]TJ/F117 9.9626 Tf 7.259 0 Td [(be)-242(as)-241(in)-242(the)-241(statement.)-242(From)]TJ ET 1 0 0 1 209.197 229.227 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -209.197 -229.227 cm BT /F117 9.9626 Tf 209.197 229.227 Td [(\0502.5\051)]TJ ET 1 0 0 1 228.286 229.227 cm 0 g 0 G 1 0 0 1 -228.286 -229.227 cm BT /F117 9.9626 Tf 230.692 229.227 Td [(and)]TJ ET 1 0 0 1 247.485 229.227 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -247.485 -229.227 cm BT /F117 9.9626 Tf 247.485 229.227 Td [(\0502.7\051)]TJ ET 1 0 0 1 266.574 229.227 cm 0 g 0 G 1 0 0 1 -266.574 -229.227 cm BT /F117 9.9626 Tf 266.574 229.227 Td [(,)-242(we)-241(deduce)-242(that)-241(for)-242(e)25(v)15(ery)]TJ/F34 9.9626 Tf 105.05 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(#)]TJ/F123 7.5716 Tf 0.205 -6.716 Td [(x)]TJ/F117 9.9626 Tf 4.958 1.611 Td [(-a.s.)-242(\002nite)]TJ ET 1 0 0 1 39.797 229.227 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -229.227 cm BT /F126 9.9626 Tf 39.797 217.272 Td [(.)]TJ/F160 9.9626 Tf 3.716 0 Td [(F)]TJ/F123 7.5716 Tf 7.161 -1.494 Td [(u)]TJ/F126 9.9626 Tf 4.685 1.494 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(-stopping)-250(time.,)]TJ ET 1 0 0 1 39.797 217.272 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -217.272 cm BT /F123 9.9626 Tf 63.976 196.459 Td [(x)]TJ/F34 9.9626 Tf 5.31 0 Td [(E)]TJ/F121 7.5716 Tf 6.642 4.115 Td [(")]TJ/F123 7.5716 Tf 0.204 -6.794 Td [(x)]TJ/F121 9.9626 Tf 4.958 2.679 Td [(T)]TJ/F123 9.9626 Tf 5.5 0 Td [(f)]TJ/F126 9.9626 Tf 4.851 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F123 7.5716 Tf 6.683 -1.494 Td [(U)]TJ/F126 9.9626 Tf 6.828 1.494 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)-278(D)]TJ/F34 9.9626 Tf 16.623 0 Td [(E)]TJ/F121 7.5716 Tf 6.642 4.115 Td [(#)]TJ/F123 7.5716 Tf 0.204 -6.794 Td [(x)]TJ/F121 9.9626 Tf 4.958 2.679 Td [(T)]TJ/F123 9.9626 Tf 4.085 0 Td [(X)]TJ/F123 7.5716 Tf 6.683 -1.494 Td [(U)]TJ/F123 9.9626 Tf 9.01 1.494 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F123 7.5716 Tf 6.683 -1.494 Td [(U)]TJ/F126 9.9626 Tf 6.828 1.494 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)]TJ/F126 9.9626 Tf 3.318 0 Td [(:)]TJ/F117 9.9626 Tf 212.037 0 Td [(\0502.9\051)]TJ ET 1 0 0 1 39.797 196.459 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -196.459 cm BT /F117 9.9626 Tf 39.797 178.002 Td [(Let)]TJ/F123 9.9626 Tf 15.771 0 Td [(t)]TJ/F121 9.9626 Tf 6.433 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0.)-250(By)-250(applying)]TJ ET 1 0 0 1 133.719 178.002 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -133.719 -178.002 cm BT /F117 9.9626 Tf 133.719 178.002 Td [(\0502.9\051)]TJ ET 1 0 0 1 152.808 178.002 cm 0 g 0 G 1 0 0 1 -152.808 -178.002 cm BT /F117 9.9626 Tf 155.298 178.002 Td [(to)-250(the)]TJ/F126 9.9626 Tf 24.907 0 Td [(.)]TJ/F160 9.9626 Tf 3.716 0 Td [(F)]TJ/F123 7.5716 Tf 7.16 -1.495 Td [(u)]TJ/F126 9.9626 Tf 4.686 1.495 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(-stopping)-250(time)]TJ ET 1 0 0 1 39.797 178.002 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -178.002 cm BT /F123 9.9626 Tf 63.976 159.544 Td [(x)]TJ/F126 7.5716 Tf 5.31 4.115 Td [(\013)]TJ/F117 9.9626 Tf 6.785 -4.115 Td [(inf)]TJ/F121 9.9626 Tf 12.729 0.115 Td [(f)]TJ/F123 9.9626 Tf 3.686 -0.115 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(V)]TJ/F126 9.9626 Tf 5.507 0 Td [(\034)-120(.)]TJ/F123 9.9626 Tf 9.225 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(/)-278(>)]TJ/F123 9.9626 Tf 17.022 0 Td [(t)]TJ/F121 9.9626 Tf 3.666 0.115 Td [(g)]TJ/F126 9.9626 Tf 5.347 -0.115 Td [(;)]TJ ET 1 0 0 1 39.797 159.544 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -159.544 cm BT /F117 9.9626 Tf 39.797 141.087 Td [(which)-250(is)]TJ/F34 9.9626 Tf 35.975 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(#)]TJ/F123 7.5716 Tf 0.204 -6.717 Td [(x)]TJ/F117 9.9626 Tf 4.958 1.612 Td [(-a.s.)-250(\002nite,)-250(and)-250(using)]TJ ET 1 0 0 1 172.531 141.087 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -172.531 -141.087 cm BT /F117 9.9626 Tf 172.531 141.087 Td [(\0502.2\051)]TJ ET 1 0 0 1 191.619 141.087 cm 0 g 0 G 1 0 0 1 -191.619 -141.087 cm BT /F117 9.9626 Tf 194.11 141.087 Td [(\050note)-250(that)]TJ/F126 9.9626 Tf 40.398 0 Td [(\034)-120(.)]TJ/F123 9.9626 Tf 9.225 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(/)]TJ/F117 9.9626 Tf 6.207 0 Td [(is)-250(continuous)-250(and)-250(increasing\051,)-250(we)-250(obtain)]TJ ET 1 0 0 1 39.797 141.087 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -141.087 cm BT /F123 9.9626 Tf 64.395 121.276 Td [(E)]TJ/F121 9.9626 Tf 6.983 0 Td [(T)]TJ/F123 9.9626 Tf 5.5 0 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(")]TJ/F123 7.5716 Tf -1.096 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)-278(D)]TJ/F123 9.9626 Tf 17.31 0 Td [(E)]TJ/F121 9.9626 Tf 6.984 0 Td [(T)]TJ/F117 9.9626 Tf 3.318 0 Td [(e)15(xp)]TJ/F126 9.9626 Tf 14.236 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(#)]TJ/F123 7.5716 Tf -1.095 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F123 9.9626 Tf 5.898 0 Td [(f)]TJ/F126 9.9626 Tf 4.851 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(#)]TJ/F123 7.5716 Tf -1.095 -7.482 Td [(t)]TJ/F126 9.9626 Tf 6.258 2.377 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(U)]TJ/F126 9.9626 Tf 3.317 0 Td [(;)]TJ ET 1 0 0 1 39.797 121.276 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -121.276 cm BT /F117 9.9626 Tf 39.797 102.818 Td [(which)-250(is)-250(the)-250(desired)-250(result.)]TJ/F116 9.9626 Tf 121.473 0 Td [(\004)]TJ ET 1 0 0 1 39.797 102.818 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -102.818 cm BT /F117 9.9626 Tf 51.752 83.836 Td [(W)80(e)-443(refer)-443(to)-443(Ri)25(v)15(ero)-444([)]TJ ET 1 0 0 1 139.031 83.836 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -139.031 -83.836 cm BT /F117 9.9626 Tf 139.031 83.836 Td [(25)]TJ ET 1 0 0 1 148.993 83.836 cm 0 g 0 G 1 0 0 1 -148.993 -83.836 cm BT /F117 9.9626 Tf 148.993 83.836 Td [(],)-443(IV)129(.6.1)-444(for)-443(a)-443(similar)-443(discussion)-443(on)-443(conditioned)-443(stable)-444(processes)]TJ ET 1 0 0 1 39.797 83.836 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -83.836 cm BT /F117 9.9626 Tf 39.797 71.881 Td [(considered)-300(as)-299(pssMp.)-300(In)-299(what)-300(follo)25(ws)-300(we)-299(call)]TJ/F126 9.9626 Tf 187.702 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F117 9.9626 Tf 4.443 -3.616 Td [(,)]TJ/F126 9.9626 Tf 5.475 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F117 9.9626 Tf 8.147 -3.616 Td [(and)]TJ/F126 9.9626 Tf 17.37 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 8.147 -3.616 Td [(the)]TJ/F123 9.9626 Tf 15.159 0 Td [(L)]TJ 6.074 -0.065 Td [(\264)]TJ -0.535 0.065 Td [(evy\226Lamperti)-300(pr)45(oces)1(ses)]TJ/F117 9.9626 Tf 96.054 0 Td [(.)-300(W)80(e)]TJ ET 1 0 0 1 39.797 71.881 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -71.881 cm BT /F117 9.9626 Tf 39.797 59.926 Td [(no)25(w)-250(compute)-250(the)-250(la)15(w)-250(of)-250(some)-250(of)-250(their)-250(functionals.)]TJ ET 1 0 0 1 39.797 59.926 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -14.112 cm 0 g 0 G 1 0 0 1 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[(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.533 1.494 Td [(/)]TJ/F117 9.9626 Tf 3.717 0 Td [(,)-318(for)]TJ/F123 9.9626 Tf 20.719 0 Td [(x)]TJ/F126 9.9626 Tf 9.337 0 Td [(>)]TJ/F117 9.9626 Tf 11.799 0 Td [(0.)-319(W)80(e)-318(denote)-318(by)]TJ/F126 9.9626 Tf 69.714 0 Td [(\030)]TJ/F117 9.9626 Tf 8.511 0 Td [(the)-318(L)]TJ 21.986 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-318(process)-319(starting)-318(from)-318(0)-318(associated)-319(to)]TJ/F123 9.9626 Tf 170.161 0 Td [(X)]TJ ET 1 0 0 1 45.354 539.138 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -539.138 cm BT /F117 9.9626 Tf 45.354 527.183 Td [(through)-250(the)-250(Lamperti)-250(transformation)]TJ ET 1 0 0 1 193.667 527.183 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -193.667 -527.183 cm BT /F117 9.9626 Tf 193.667 527.183 Td [(\0502.2\051)]TJ ET 1 0 0 1 212.755 527.183 cm 0 g 0 G 1 0 0 1 -212.755 -527.183 cm BT /F117 9.9626 Tf 215.246 527.183 Td [(with)-250(reference)-250(measure)]TJ/F123 9.9626 Tf 96.307 0 Td [(P)]TJ/F117 9.9626 Tf 9.395 0 Td [(on)]TJ/F160 9.9626 Tf 12.453 0 Td [(D)]TJ/F117 9.9626 Tf 7.962 0 Td [(.)-250(F)15(or)-250(an)15(y)]TJ/F123 9.9626 Tf 38.526 0 Td [(y)]TJ/F121 9.9626 Tf 7.709 0 Td [(2)]TJ/F34 9.9626 Tf 9.033 0 Td [(R)]TJ/F117 9.9626 Tf 9.686 0 Td [(let)]TJ ET 1 0 0 1 45.354 527.183 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -527.183 cm BT /F123 9.9626 Tf 69.494 508.873 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.408 -6.795 Td [(y)]TJ/F121 9.9626 Tf 10.58 2.68 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F121 9.9626 Tf 11.068 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F121 9.9626 Tf 6.434 0 Td [(V)]TJ/F126 9.9626 Tf 5.507 0 Td [(\030)]TJ/F123 7.5716 Tf 4.244 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.494 Td [(\025)]TJ/F123 9.9626 Tf 10.917 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(g)]TJ/F117 9.9626 Tf 13.649 0 Td [(and)]TJ/F123 9.9626 Tf 24.578 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(\000)]TJ/F123 7.5716 Tf -1.408 -6.795 Td [(y)]TJ/F121 9.9626 Tf 10.58 2.68 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F121 9.9626 Tf 11.068 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F121 9.9626 Tf 6.434 0 Td [(V)]TJ/F126 9.9626 Tf 5.507 0 Td [(\030)]TJ/F123 7.5716 Tf 4.244 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.494 Td [(\024)]TJ/F123 9.9626 Tf 10.917 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(g)]TJ/F126 9.9626 Tf 3.686 0 Td [(;)]TJ ET 1 0 0 1 45.354 508.873 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -508.873 cm BT /F117 9.9626 Tf 45.354 490.563 Td [(and)-250(for)-250(an)15(y)]TJ/F123 9.9626 Tf 48.349 0 Td [(y)]TJ/F126 9.9626 Tf 7.709 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)-250(let)]TJ ET 1 0 0 1 45.354 490.563 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -490.563 cm BT /F126 9.9626 Tf 69.265 472.253 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.114 Td [(C)]TJ/F123 7.5716 Tf -0.811 -6.794 Td [(y)]TJ/F121 9.9626 Tf 9.982 2.68 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F121 9.9626 Tf 11.069 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F121 9.9626 Tf 6.433 0 Td [(V)]TJ/F123 9.9626 Tf 6.275 0 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.494 Td [(\025)]TJ/F123 9.9626 Tf 10.917 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(g)]TJ/F117 9.9626 Tf 13.649 0 Td [(and)]TJ/F126 9.9626 Tf 24.349 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.114 Td [(\000)]TJ/F123 7.5716 Tf -0.811 -6.794 Td [(y)]TJ/F121 9.9626 Tf 9.982 2.68 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F121 9.9626 Tf 11.069 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F121 9.9626 Tf 6.433 0 Td [(V)]TJ/F123 9.9626 Tf 6.274 0 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.494 Td [(t)]TJ/F121 9.9626 Tf 6.052 1.494 Td [(\024)]TJ/F123 9.9626 Tf 10.917 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(g)]TJ/F126 9.9626 Tf 3.686 0 Td [(:)]TJ ET 1 0 0 1 45.354 472.253 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -29.252 cm 0 g 0 G 1 0 0 1 -41.369 -443.001 cm BT /F124 9.9626 Tf 45.354 443.001 Td [(Lemma)-250(1.)]TJ ET 1 0 0 1 87.964 443.001 cm 0 g 0 G 1 0 0 1 -87.964 -443.001 cm BT /F123 9.9626 Tf 91.949 443.001 Td [(F)45(ix)]TJ/F121 9.9626 Tf 15.491 0 Td [(\0001)]TJ/F126 9.9626 Tf 20.965 0 Td [(<)-303(v)-344(<)]TJ/F117 9.9626 Tf 29.861 0 Td [(0)]TJ/F126 9.9626 Tf 8.004 0 Td [(<)]TJ/F123 9.9626 Tf 10.794 0 Td [(u)]TJ/F126 9.9626 Tf 8.532 0 Td [(<)]TJ/F121 9.9626 Tf 10.794 0 Td [(1)]TJ/F123 9.9626 Tf 10.172 0 Td [(.)-264(Suppose)-264(that)-381(A)-283(is)-264(any)-264(interval)-264(in)]TJ/F121 9.9626 Tf 139.454 0 Td [(T)]TJ/F123 9.9626 Tf 3.318 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(;)]TJ/F121 9.9626 Tf 4.958 0 Td [(1)]TJ/F126 9.9626 Tf 10.172 0 Td [(/)]TJ/F123 9.9626 Tf 6.345 0 Td [(and)-367(B)-327(is)-264(any)]TJ ET 1 0 0 1 45.354 443.001 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -443.001 cm BT /F123 9.9626 Tf 45.354 431.046 Td [(interval)-250(in)]TJ/F126 9.9626 Tf 43.726 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\0001)]TJ/F126 9.9626 Tf 17.942 0 Td [(;)-167(v)]TJ/F121 9.9626 Tf 10.209 0 Td [(U)]TJ/F123 9.9626 Tf 3.317 0 Td [(.)-250(Then,)]TJ ET 1 0 0 1 45.354 431.046 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -431.046 cm BT /F123 9.9626 Tf 70.141 411.501 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.998 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.998 Td [(\030)]TJ/F123 7.5716 Tf 4.419 -3.096 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(C)]TJ/F123 5.9776 Tf -1.439 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.865 4.422 Td [(2)]TJ/F123 9.9626 Tf 10.02 0 Td [(A)]TJ/F121 9.9626 Tf 6.286 0 Td [(I)]TJ/F123 9.9626 Tf 5.447 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.065 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(\000)]TJ/F126 7.5716 Tf -1.892 -6.794 Td [(v)]TJ/F151 9.9626 Tf 8.296 13.678 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.998 Td [(D)]TJ/F34 9.9626 Tf 10.539 0 Td [(P)]TJ/F117 7.5716 Tf 6.088 -1.498 Td [(1)]TJ/F151 9.9626 Tf 5.944 12.496 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.998 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.282 Td [(C)]TJ/F117 5.9776 Tf -0.984 -6.337 Td [(e)]TJ/F123 5.9776 Tf 2.654 1.728 Td [(u)]TJ/F121 9.9626 Tf 7.567 4.422 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(e)]TJ/F123 7.5716 Tf 5.173 4.114 Td [(A)]TJ/F121 9.9626 Tf 5.276 -4.114 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.294 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.369 Td [(e)]TJ/F123 5.9776 Tf 3.361 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.105 0.887 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.279 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.188 Td [(v)]TJ/F151 9.9626 Tf 4.337 11.796 Td [(\021)]TJ ET 1 0 0 1 45.354 411.501 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -411.501 cm BT /F123 9.9626 Tf 45.354 391.851 Td [(and)]TJ ET 1 0 0 1 45.354 391.851 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -391.851 cm BT /F123 9.9626 Tf 70.141 374.537 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(\030)]TJ/F123 7.5716 Tf 4.419 -3.095 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 9.9626 Tf 9.865 4.332 Td [(2)]TJ/F123 9.9626 Tf 9.791 0 Td [(B)]TJ/F121 9.9626 Tf 6.715 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F34 9.9626 Tf 10.538 0 Td [(P)]TJ/F117 7.5716 Tf 6.088 -1.497 Td [(1)]TJ/F151 9.9626 Tf 5.944 12.496 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.999 Td [(X)]TJ/F126 7.5716 Tf 6.805 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.027 3.282 Td [(\000)]TJ/F117 5.9776 Tf -0.984 -6.247 Td [(e)]TJ/F126 5.9776 Tf 2.654 1.728 Td [(v)]TJ/F121 9.9626 Tf 7.412 4.332 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(e)]TJ/F123 7.5716 Tf 4.999 4.115 Td [(B)]TJ/F121 9.9626 Tf 5.601 -4.115 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.37 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.104 0.887 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.154 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.28 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.188 Td [(v)]TJ/F151 9.9626 Tf 4.338 11.796 Td [(\021)]TJ/F126 9.9626 Tf 7.09 -10.999 Td [(:)]TJ ET 1 0 0 1 45.354 374.537 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -374.537 cm BT /F117 9.9626 Tf 57.31 350.327 Td [(The)-252(proof)-252(is)-251(a)-252(straightforw)10(ard)-252(consequence)-252(of)-252(the)-251(Lamperti)-252(representation)]TJ ET 1 0 0 1 356.187 350.327 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -356.187 -350.327 cm BT /F117 9.9626 Tf 356.187 350.327 Td [(\0502.2\051)]TJ ET 1 0 0 1 375.275 350.327 cm 0 g 0 G 1 0 0 1 -375.275 -350.327 cm BT /F117 9.9626 Tf 377.784 350.327 Td [(and)-252(is)-252(left)-251(as)]TJ ET 1 0 0 1 45.354 350.327 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -350.327 cm BT /F117 9.9626 Tf 45.354 338.372 Td [(an)-214(e)15(x)15(ercise.)-213(Although)-214(some)25(what)-213(ob)15(vious,)-214(this)-213(lemma)-214(indicates)-213(that)-214(for)-213(the)-213(three)-214(processes)]TJ/F126 9.9626 Tf 357.323 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.616 Td [(;)-167(\030)]TJ/F121 7.5716 Tf 10.298 3.616 Td [(\003)]TJ ET 1 0 0 1 45.354 338.372 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -338.372 cm BT /F117 9.9626 Tf 45.354 326.417 Td [(and)]TJ/F126 9.9626 Tf 16.425 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 5.162 -3.616 Td [(,)-205(we)-204(need)-205(to)-205(understand)-204(ho)25(w)65(,)-205(respecti)25(v)15(ely)65(,)-205(an)]TJ/F126 9.9626 Tf 178.433 0 Td [(\013)]TJ/F117 9.9626 Tf 6.087 0 Td [(-stable)-205(process)-204(conditioned)-205(to)-205(st)1(ay)-205(positi)25(v)15(e,)]TJ ET 1 0 0 1 45.354 326.417 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -326.417 cm BT /F117 9.9626 Tf 45.354 314.462 Td [(an)]TJ/F126 9.9626 Tf 11.67 0 Td [(\013)]TJ/F117 9.9626 Tf 6.088 0 Td [(-stable)-227(process)-228(killed)-227(when)-227(it)-228(e)15(xits)-227(the)-228(positi)25(v)15(e)-227(half-line)-227(and)-228(an)]TJ/F126 9.9626 Tf 250.709 0 Td [(\013)]TJ/F117 9.9626 Tf 6.087 0 Td [(-stable)-227(process)-228(conditioned)]TJ ET 1 0 0 1 45.354 314.462 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -314.462 cm BT /F117 9.9626 Tf 45.354 302.506 Td [(to)-284(hit)-285(the)-284(origin)-284(continuously)65(,)-285(e)15(xit)-284(a)-285(positi)25(v)15(e)-284(interv)25(al)-284(around)]TJ/F123 9.9626 Tf 244.39 0 Td [(x)]TJ/F126 9.9626 Tf 8.711 0 Td [(>)]TJ/F117 9.9626 Tf 11.173 0 Td [(0.)-285(F)15(ortunately)-284(this)-284(is)-285(possible)]TJ ET 1 0 0 1 45.354 302.506 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -302.506 cm BT /F117 9.9626 Tf 45.354 290.551 Td [(thanks)-250(to)-250(a)-250(result)-250(of)-250(Rogozin)-250([)]TJ ET 1 0 0 1 166.001 290.551 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -166.001 -290.551 cm BT /F117 9.9626 Tf 166.001 290.551 Td [(27)]TJ ET 1 0 0 1 175.963 290.551 cm 0 g 0 G 1 0 0 1 -175.963 -290.551 cm BT /F117 9.9626 Tf 175.963 290.551 Td [(])-250(who)-250(established)-250(the)-250(follo)25(wing)-250(for)]TJ/F126 9.9626 Tf 141.976 0 Td [(\013)]TJ/F117 9.9626 Tf 6.088 0 Td [(-stable)-250(processes.)]TJ ET 1 0 0 1 45.354 290.551 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -20.844 cm 0 g 0 G 1 0 0 1 -41.369 -269.707 cm BT /F124 9.9626 Tf 45.354 269.707 Td [(Theor)18(em)-250(1)]TJ ET 1 0 0 1 91.381 269.707 cm 0 g 0 G 1 0 0 1 -91.381 -269.707 cm BT /F117 9.9626 Tf 95.366 269.707 Td [(\050)]TJ/F123 9.9626 Tf 3.318 0 Td [(Ro)10(gozin)-234([)]TJ ET 1 0 0 1 137.445 269.707 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -137.445 -269.707 cm BT /F123 9.9626 Tf 137.445 269.707 Td [(27)]TJ ET 1 0 0 1 147.408 269.707 cm 0 g 0 G 1 0 0 1 -147.408 -269.707 cm BT /F123 9.9626 Tf 147.408 269.707 Td [(])]TJ/F117 9.9626 Tf 3.875 0 Td [(\051.)]TJ/F123 9.9626 Tf 8.136 0 Td [(Suppose)-234(that)]TJ/F126 9.9626 Tf 53.542 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F124 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(/)]TJ/F123 9.9626 Tf 6.044 0 Td [(is)-234(an)]TJ/F126 9.9626 Tf 21.263 0 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(-stable)-234(pr)45(ocess,)-233(initiated)-234(fr)45(om)-261(x)-89(,)-233(whic)15(h)]TJ ET 1 0 0 1 45.354 269.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -269.707 cm BT /F123 9.9626 Tf 45.354 257.752 Td [(has)-250(two-sided)-250(jumps.)-250(Denoting)]TJ/F126 9.9626 Tf 125.917 0 Td [(\032)]TJ/F121 9.9626 Tf 8.795 0 Td [(D)]TJ/F124 9.9626 Tf 10.538 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(0)]TJ/F126 9.9626 Tf 4.284 1.498 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F117 7.5716 Tf 6.805 -1.498 Td [(1)]TJ/F126 9.9626 Tf 7.051 1.498 Td [(<)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F123 9.9626 Tf 6.207 0 Td [(we)-250(have)-250(for)-270(a)]TJ/F126 9.9626 Tf 57.402 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F123 9.9626 Tf 7.472 0 Td [(and)-304(x)]TJ/F121 9.9626 Tf 26.05 0 Td [(2)]TJ/F126 9.9626 Tf 9.034 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F123 9.9626 Tf 4.928 0 Td [(a)]TJ/F126 9.9626 Tf 5.46 0 Td [(/)]TJ/F123 9.9626 Tf 3.716 0 Td [(,)]TJ ET 1 0 0 1 45.354 257.752 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -257.752 cm BT /F124 9.9626 Tf 69.265 237.883 Td [(P)]TJ/F123 7.5716 Tf 6.291 -1.495 Td [(x)]TJ/F151 9.9626 Tf 6.194 12.493 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.998 Td [(X)]TJ/F126 7.5716 Tf 6.805 -3.096 Td [(\033)]TJ/F121 5.9776 Tf 5.027 3.283 Td [(C)]TJ/F123 5.9776 Tf -1.002 -4.609 Td [(a)]TJ/F121 9.9626 Tf 8.875 4.422 Td [(\000)]TJ/F123 9.9626 Tf 9.955 0 Td [(a)]TJ/F121 9.9626 Tf 8.227 0 Td [(2)]TJ/F117 9.9626 Tf 9.033 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 4.942 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.318 -6.794 Td [(a)]TJ/F126 9.9626 Tf 10.489 2.68 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.154 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.625 Td [(0)]TJ/F151 9.9626 Tf 7.699 14.329 Td [(\021)]TJ ET 1 0 0 1 45.354 237.883 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -237.883 cm BT /F121 9.9626 Tf 79.227 213.594 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 216.084 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 206.52 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F123 9.9626 Tf 3.686 0 Td [(a)]TJ/F121 9.9626 Tf 7.673 0 Td [(\000)]TJ/F123 9.9626 Tf 10.254 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F123 9.9626 Tf 8.172 -4.114 Td [(x)]TJ/F126 7.5716 Tf 5.31 4.114 Td [(\013)40(\032)]TJ/F123 9.9626 Tf 9.737 -4.114 Td [(y)]TJ/F121 7.5716 Tf 4.942 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F123 9.9626 Tf 4.353 0 Td [(y)]TJ/F121 9.9626 Tf 7.156 0 Td [(C)]TJ/F123 9.9626 Tf 9.955 0 Td [(a)]TJ/F126 9.9626 Tf 5.459 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.114 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F123 9.9626 Tf 9.955 0 Td [(a)]TJ/F121 9.9626 Tf 7.674 0 Td [(\000)]TJ/F123 9.9626 Tf 10.253 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(:)]TJ ET 1 0 0 1 45.354 213.594 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -213.594 cm BT /F117 9.9626 Tf 57.31 186.73 Td [(Note)-394(that)-395(an)-394(e)15(xpression)-394(for)]TJ/F124 9.9626 Tf 117.434 0 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 8.538 0 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.282 Td [(\000)]TJ/F117 5.9776 Tf -0.985 -5.966 Td [(0)]TJ/F121 9.9626 Tf 12.073 5.779 Td [(2)]TJ/F117 9.9626 Tf 11.697 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 3.616 Td [(C)]TJ/F123 7.5716 Tf -1.317 -6.296 Td [(a)]TJ/F126 9.9626 Tf 13.151 2.68 Td [(>)-545(\033)]TJ/F121 7.5716 Tf 19.816 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.625 Td [(0)]TJ/F126 9.9626 Tf 7.699 3.331 Td [(/)]TJ/F117 9.9626 Tf 7.645 0 Td [(can)-394(be)-395(deri)25(v)15(ed)-394(from)-394(the)-395(abo)15(v)15(e)]TJ ET 1 0 0 1 45.354 186.73 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -186.73 cm BT /F117 9.9626 Tf 45.354 173.077 Td [(e)15(xpression)-250(by)-250(replacing)]TJ/F123 9.9626 Tf 97.235 0 Td [(x)]TJ/F117 9.9626 Tf 7.801 0 Td [(by)]TJ/F123 9.9626 Tf 12.423 0 Td [(a)]TJ/F121 9.9626 Tf 7.673 0 Td [(\000)]TJ/F123 9.9626 Tf 10.254 0 Td [(x)]TJ/F117 9.9626 Tf 7.801 0 Td [(and)]TJ/F126 9.9626 Tf 16.877 0 Td [(\032)]TJ/F117 9.9626 Tf 8.518 0 Td [(by)-250(1)]TJ/F121 9.9626 Tf 19.648 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)]TJ/F117 9.9626 Tf 6.027 0 Td [(.)]TJ ET 1 0 0 1 45.354 173.077 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -173.077 cm BT /F117 9.9626 Tf 57.31 161.276 Td [(In)-235(what)-235(follo)25(ws,)-234(with)-235(an)-235(ab)20(use)-235(of)-235(notation,)-234(we)-235(will)-235(denote)-235(by)]TJ/F123 9.9626 Tf 244.788 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 3.617 Td [(C)]TJ/F123 7.5716 Tf -1.408 -6.297 Td [(y)]TJ/F117 9.9626 Tf 10.152 2.68 Td [(and)]TJ/F123 9.9626 Tf 16.954 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 3.617 Td [(\000)]TJ/F123 7.5716 Tf -1.409 -6.297 Td [(y)]TJ/F117 9.9626 Tf 10.152 2.68 Td [(for)-235(the)-235(\002rst)-234(passage)]TJ ET 1 0 0 1 45.354 161.276 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -161.276 cm BT /F117 9.9626 Tf 45.354 147.404 Td [(times)-258(abo)15(v)15(e)-258(and)-258(belo)25(w)]TJ/F123 9.9626 Tf 94.489 0 Td [(y)]TJ/F121 9.9626 Tf 7.859 0 Td [(2)]TJ/F34 9.9626 Tf 9.183 0 Td [(R)]TJ/F117 9.9626 Tf 7.195 0 Td [(,)-258(respecti)25(v)15(ely)65(,)-258(of)-258(the)-258(processes)]TJ/F126 9.9626 Tf 123.581 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.616 Td [(;)-167(\030)]TJ/F121 7.5716 Tf 10.298 3.616 Td [(\003)]TJ/F117 9.9626 Tf 7.014 -3.616 Td [(or)]TJ/F126 9.9626 Tf 10.871 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 7.733 -3.616 Td [(depending)-258(on)-258(the)-258(case)]TJ ET 1 0 0 1 45.354 147.404 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -147.404 cm BT /F117 9.9626 Tf 45.354 135.449 Td [(that)-250(we)-250(are)-250(studying.)]TJ ET 1 0 0 1 45.354 135.449 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -135.449 cm BT /F117 9.9626 Tf 57.31 123.648 Td [(W)80(e)-269(no)25(w)-269(proceed)-268(to)-269(split)-269(the)-269(remainder)-269(of)-268(this)-269(section)-269(into)-269(three)-269(subsections)-269(dea)1(ling)-269(with)-269(the)]TJ ET 1 0 0 1 45.354 123.648 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -123.648 cm BT /F117 9.9626 Tf 45.354 111.693 Td [(tw)10(o-sided)-250(e)15(xit)-250(problem)-250(and)-250(its)-250(rami\002cations)-250(for)-250(the)-250(three)-250(processes)]TJ/F126 9.9626 Tf 269.805 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F126 9.9626 Tf 5.163 -3.617 Td [(;)-167(\030)]TJ/F121 7.5716 Tf 10.298 3.617 Td [(\003)]TJ/F117 9.9626 Tf 6.933 -3.617 Td [(and)]TJ/F126 9.9626 Tf 16.877 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(#)]TJ/F117 9.9626 Tf 7.653 -3.617 Td [(respecti)25(v)15(ely)65(.)]TJ ET 1 0 0 1 45.354 111.693 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -111.693 cm BT /F123 9.9626 Tf 45.354 90.627 Td [(3.1.)-500(Calculations)-250(for)]TJ/F126 9.9626 Tf 87.461 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ ET 1 0 0 1 45.354 90.627 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -90.627 cm BT /F117 9.9626 Tf 57.31 69.724 Td [(The)-237(tw)10(o-sided)-236(e)15(xit)-237(problem)-236(for)]TJ/F126 9.9626 Tf 126.087 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F117 9.9626 Tf 7.52 -3.616 Td [(can)-237(be)-236(obtained)-237(from)]TJ ET 1 0 0 1 282.598 69.724 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -282.598 -69.724 cm BT /F117 9.9626 Tf 282.598 69.724 Td [(Lemma)-237(1)]TJ ET 1 0 0 1 320.372 69.724 cm 0 g 0 G 1 0 0 1 -320.372 -69.724 cm BT /F117 9.9626 Tf 322.73 69.724 Td [(and)]TJ ET 1 0 0 1 339.473 69.724 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -339.473 -69.724 cm BT /F117 9.9626 Tf 339.473 69.724 Td [(Theorem)-237(1)]TJ ET 1 0 0 1 382.777 69.724 cm 0 g 0 G 1 0 0 1 -382.777 -69.724 cm BT /F117 9.9626 Tf 385.134 69.724 Td [(as)-237(follo)25(ws.)]TJ ET 1 0 0 1 45.354 69.724 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -69.724 cm BT /F117 9.9626 Tf 45.354 57.769 Td [(W)80(e)-264(gi)25(v)15(e)-263(the)-264(case)-263(for)-264(tw)10(o-sided)-264(jumps.)-263(Note)-264(that)-263(this)-264(is)-264(more)-263(for)-527(con)40(v)15(enience)-264(than)-264(a)-263(restriction.)]TJ ET 1 0 0 1 45.354 45.814 cm 0 g 0 G 1 0 0 1 382.566 0 cm 0 g 0 G endstream endobj 47 0 obj <> endobj 48 0 obj <> /Type /Annot /C [ 1 0 0 ] /Border [ 0 0 0 ] /Subtype /Link /Rect [ 307.041 375.695 346.713 386.639 ] >> endobj 49 0 obj <> /ProcSet [ /PDF /Text ] >> endobj 50 0 obj <>stream 1 0 0 1 39.797 629.624 cm 0 g 0 G 1 0 0 1 -39.797 -629.624 cm BT /F117 7.9701 Tf 39.797 629.624 Td [(986)]TJ/F123 7.9701 Tf 59.131 0 Td [(L.)-250(Chaumont)-250(et)-250(al.)-250(/)-250(Stoc)15(hastic)-250(Pr)45(ocesses)-250(and)-250(their)-250(Applications)-250(119)-250(\0502009\051)-250(980\2261000)]TJ ET 1 0 0 1 422.362 629.624 cm 0 g 0 G 1 0 0 1 -422.362 -629.624 cm BT /F117 9.9626 Tf 39.797 607.707 Td [(By)-272(taki)1(ng)-272(limits)-272(as)]TJ/F126 9.9626 Tf 78.356 0 Td [(\013)-40(.)]TJ/F117 9.9626 Tf 9.803 0 Td [(1)]TJ/F121 9.9626 Tf 7.354 0 Td [(\000)]TJ/F126 9.9626 Tf 10.144 0 Td [(\032)-60(/)]TJ/F121 9.9626 Tf 12.908 0 Td [(!)]TJ/F117 9.9626 Tf 14.113 0 Td [(1)-272(or)]TJ/F126 9.9626 Tf 18.691 0 Td [(\013)40(\032)]TJ/F121 9.9626 Tf 14.482 0 Td [(!)]TJ/F117 9.9626 Tf 14.113 0 Td [(1)-272(in)-271(the)-272(gi)25(v)15(en)-271(e)15(xpressions)-272(we)-271(deduce)-272(identities)-271(for)]TJ ET 1 0 0 1 39.797 607.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -607.707 cm BT /F117 9.9626 Tf 39.797 595.751 Td [(the)-284(case)-285(that)]TJ/F126 9.9626 Tf 52.763 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F117 9.9626 Tf 7.995 -3.617 Td [(is)-284(spectrally)-285(ne)15(g)5(ati)25(v)15(e)-284(and)-285(spectrally)-284(positi)25(v)15(e)-284(respecti)25(v)15(ely)65(.)-285(Note)-284(that)-285(necessarily)]TJ ET 1 0 0 1 39.797 595.751 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -595.751 cm BT /F117 9.9626 Tf 39.797 583.796 Td [(in)-250(the)-250(spectrally)-250(one-sided)-250(case)]TJ/F126 9.9626 Tf 126.992 0 Td [(\013)]TJ/F121 9.9626 Tf 8.855 0 Td [(2)]TJ/F126 9.9626 Tf 9.033 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(2)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(.)]TJ ET 1 0 0 1 39.797 583.796 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.215 cm 0 g 0 G 1 0 0 1 -35.812 -561.581 cm BT /F124 9.9626 Tf 39.797 561.581 Td [(Theor)18(em)-250(2.)]TJ ET 1 0 0 1 88.315 561.581 cm 0 g 0 G 1 0 0 1 -88.315 -561.581 cm BT /F123 9.9626 Tf 92.3 561.581 Td [(F)45(ix)]TJ/F126 9.9626 Tf 15.352 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F123 9.9626 Tf 7.472 0 Td [(and)]TJ/F121 9.9626 Tf 17.704 0 Td [(\0001)]TJ/F126 9.9626 Tf 20.71 0 Td [(<)-278(v)-318(<)]TJ/F117 9.9626 Tf 29.094 0 Td [(0)]TJ/F126 9.9626 Tf 7.748 0 Td [(<)]TJ/F123 9.9626 Tf 10.538 0 Td [(u)]TJ/F126 9.9626 Tf 8.277 0 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F123 9.9626 Tf 10.172 0 Td [(.)]TJ ET 1 0 0 1 39.797 561.581 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -561.581 cm BT /F123 9.9626 Tf 64.584 541.683 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.922 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.438 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.311 6.255 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F121 9.9626 Tf 8.276 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ/F121 9.9626 Tf 5.379 0 Td [(I)]TJ/F123 9.9626 Tf 5.447 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.794 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 39.797 541.683 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -541.683 cm BT /F121 9.9626 Tf 73.67 517.394 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 85.404 519.885 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 110.41 510.32 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.9 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ ET 1 0 0 1 39.797 517.394 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -517.394 cm BT /F121 9.9626 Tf 83.632 496.87 Td [(\002)]TJ/F126 9.9626 Tf 9.472 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F121 7.5716 Tf 8.601 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.8 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ ET 1 0 0 1 39.797 496.87 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -496.87 cm BT /F123 9.9626 Tf 39.797 478.804 Td [(and)]TJ ET 1 0 0 1 39.797 478.804 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -478.804 cm BT /F123 9.9626 Tf 64.584 460.739 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.998 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.998 Td [(v)]TJ/F121 9.9626 Tf 7.464 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.922 -10.034 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.519 Td [(v)]TJ/F121 9.9626 Tf 9.864 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.794 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.678 Td [(\021)]TJ ET 1 0 0 1 39.797 460.739 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -460.739 cm BT /F121 9.9626 Tf 73.67 436.5 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-100(\013)40(\032)]TJ ET q 1 0 0 1 85.404 438.99 cm []0 d 0 J 0.458 w 0 0 m 31.578 0 l S Q BT /F126 9.9626 Tf 97.706 429.426 Td [(\031)]TJ 20.471 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ ET 1 0 0 1 39.797 436.5 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -436.5 cm BT /F121 9.9626 Tf 83.632 415.976 Td [(\002)]TJ/F126 9.9626 Tf 9.472 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F121 7.5716 Tf 8.601 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 9.9626 Tf 6.703 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.283 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)-87(:)]TJ ET 1 0 0 1 39.797 415.976 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -25.173 cm 0 g 0 G 1 0 0 1 -35.812 -390.803 cm BT /F124 9.9626 Tf 39.797 390.803 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 65.75 390.803 cm 0 g 0 G 1 0 0 1 -65.75 -390.803 cm BT /F117 9.9626 Tf 69.735 390.803 Td [(Recall)-330(that)]TJ/F126 9.9626 Tf 46.974 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F124 9.9626 Tf 4.958 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(/)]TJ/F117 9.9626 Tf 7.004 0 Td [(denotes)-330(an)]TJ/F126 9.9626 Tf 46.417 0 Td [(\013)]TJ/F117 9.9626 Tf 6.087 0 Td [(-stable)-330(process)-330(initiated)-330(from)-330(1)-330(and)-330(that)]TJ/F126 9.9626 Tf 165.79 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(")]TJ/F117 7.5716 Tf 0 -8.435 Td [(1)]TJ/F126 9.9626 Tf 5.162 3.33 Td [(/)]TJ/F117 9.9626 Tf 7.005 0 Td [(is)-330(an)]TJ ET 1 0 0 1 39.797 390.803 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -390.803 cm BT /F126 9.9626 Tf 39.797 378.848 Td [(\013)]TJ/F117 9.9626 Tf 6.087 0 Td [(-stable)-227(process)-227(conditioned)-227(to)-228(stay)-227(positi)25(v)15(e)-227(initiated)-227(from)-227(1.)-228(From)]TJ ET 1 0 0 1 308.037 378.848 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -308.037 -378.848 cm BT /F117 9.9626 Tf 308.037 378.848 Td [(Lemma)-227(1)]TJ ET 1 0 0 1 345.717 378.848 cm 0 g 0 G 1 0 0 1 -345.717 -378.848 cm BT /F117 9.9626 Tf 345.717 378.848 Td [(,)-227(we)-227(ha)20(v)15(e)-228(for)]TJ/F126 9.9626 Tf 53.238 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ ET 1 0 0 1 39.797 378.848 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -378.848 cm BT /F123 9.9626 Tf 64.584 358.128 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.922 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.438 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.864 6.255 Td [(\024)]TJ/F123 9.9626 Tf 10.28 0 Td [(u)]TJ/F121 9.9626 Tf 7.723 0 Td [(C)]TJ/F126 9.9626 Tf 9.985 0 Td [(\022)]TJ/F121 9.9626 Tf 5.379 0 Td [(I)]TJ/F123 9.9626 Tf 5.447 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.114 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.794 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 39.797 358.128 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -358.128 cm BT /F121 9.9626 Tf 73.67 336.21 Td [(D)]TJ/F34 9.9626 Tf 10.538 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(")]TJ/F117 7.5716 Tf 0 -8.436 Td [(1)]TJ/F151 9.9626 Tf 6.823 14.33 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.999 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.282 Td [(C)]TJ/F117 5.9776 Tf -0.985 -6.336 Td [(e)]TJ/F123 5.9776 Tf 2.654 1.727 Td [(u)]TJ/F121 9.9626 Tf 7.568 4.422 Td [(2)-278(T)]TJ/F117 9.9626 Tf 12.351 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F126 9.9626 Tf 4.686 -4.115 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 4.587 -4.115 Td [(UI)]TJ/F126 9.9626 Tf 10.195 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.37 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.104 0.887 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.154 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.28 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.188 Td [(v)]TJ/F151 9.9626 Tf 4.338 11.796 Td [(\021)]TJ ET 1 0 0 1 39.797 336.21 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -336.21 cm BT /F121 9.9626 Tf 73.67 308.419 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.922 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.748 Td [(u)]TJ/F121 5.9776 Tf 3.306 0 Td [(C)]TJ/F126 5.9776 Tf 4.662 0 Td [(\022)]TJ/F121 7.5716 Tf 3.726 -2.748 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.748 Td [(u)]TJ/F117 7.5716 Tf -28.887 -22.341 Td [(0)]TJ/F126 9.9626 Tf 33.188 8.956 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.115 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F124 9.9626 Tf 9.099 -4.115 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(1)]TJ/F151 9.9626 Tf 5.945 12.496 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.999 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.282 Td [(C)]TJ/F117 5.9776 Tf -0.985 -6.336 Td [(e)]TJ/F123 5.9776 Tf 2.654 1.727 Td [(u)]TJ/F121 9.9626 Tf 7.014 4.422 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 7.453 -4.115 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.37 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.105 0.887 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.28 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.188 Td [(v)]TJ/F151 9.9626 Tf 4.337 11.796 Td [(\021)]TJ ET 1 0 0 1 39.797 308.419 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -308.419 cm BT /F121 9.9626 Tf 73.67 278.041 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.56 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.923 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.748 Td [(u)]TJ/F121 5.9776 Tf 3.306 0 Td [(C)]TJ/F126 5.9776 Tf 4.662 0 Td [(\022)]TJ/F121 7.5716 Tf 3.726 -2.748 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.748 Td [(u)]TJ/F117 7.5716 Tf -28.887 -22.341 Td [(0)]TJ/F126 9.9626 Tf 33.188 8.956 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.115 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F124 9.9626 Tf 9.099 -4.115 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.188 Td [(v)]TJ/F151 9.9626 Tf 5.807 10.308 Td [(\020)]TJ/F123 9.9626 Tf 6.196 -10.999 Td [(X)]TJ/F126 7.5716 Tf 6.805 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.027 3.283 Td [(C)]TJ/F126 5.9776 Tf -0.984 -6.337 Td [(.)]TJ/F117 5.9776 Tf 2.23 0 Td [(e)]TJ/F123 5.9776 Tf 2.654 1.728 Td [(u)]TJ/F121 5.9776 Tf 3.804 -1.728 Td [(\000)]TJ/F117 5.9776 Tf 4.662 0 Td [(e)]TJ/F126 5.9776 Tf 2.654 1.728 Td [(v)]TJ 3.648 -1.728 Td [(/)]TJ/F121 9.9626 Tf 5.44 6.149 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.115 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 4.941 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.616 4.295 Td [(C)]TJ/F126 7.5716 Tf -1.296 -7.663 Td [(.)]TJ/F117 7.5716 Tf 2.825 0 Td [(e)]TJ/F123 5.9776 Tf 3.361 2.188 Td [(u)]TJ/F121 7.5716 Tf 3.804 -2.188 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.188 Td [(v)]TJ/F126 7.5716 Tf 3.648 -2.188 Td [(/)]TJ/F126 9.9626 Tf 6.09 3.368 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.625 Td [(0)]TJ/F151 9.9626 Tf 7.699 14.329 Td [(\021)]TJ ET 1 0 0 1 39.797 278.041 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -278.041 cm BT /F121 9.9626 Tf 73.67 251.166 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 85.404 253.657 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 110.41 244.092 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.9 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ ET 1 0 0 1 39.797 251.166 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -251.166 cm BT /F121 9.9626 Tf 83.632 222.628 Td [(\002)]TJ/F151 9.9626 Tf 11.132 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.923 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.749 Td [(u)]TJ/F121 5.9776 Tf 3.305 0 Td [(C)]TJ/F126 5.9776 Tf 4.663 0 Td [(\022)]TJ/F121 7.5716 Tf 3.726 -2.749 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.749 Td [(u)]TJ/F117 7.5716 Tf -28.887 -22.342 Td [(0)]TJ/F126 9.9626 Tf 33.188 8.957 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F126 9.9626 Tf 4.686 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F123 9.9626 Tf 9.737 -4.114 Td [(y)]TJ/F121 7.5716 Tf 4.941 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.9 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.114 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.717 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ ET 1 0 0 1 39.797 222.628 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -222.628 cm BT /F117 9.9626 Tf 39.797 199.664 Td [(from)-250(which)-250(the)-250(\002rst)-250(part)-250(of)-250(the)-250(theorem)-250(follo)25(ws.)]TJ ET 1 0 0 1 39.797 199.664 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -199.664 cm BT /F117 9.9626 Tf 51.752 187.643 Td [(The)-250(second)-250(part)-250(of)-250(the)-250(theorem)-250(can)-250(be)-250(pro)15(v)15(ed)-250(in)-250(a)-250(similar)-250(w)10(ay)65(.)-250(Indeed)-250(for)]TJ/F126 9.9626 Tf 296.645 0 Td [(\022)]TJ/F121 9.9626 Tf 8.148 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ ET 1 0 0 1 39.797 187.643 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -187.643 cm BT /F123 9.9626 Tf 64.584 166.922 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.922 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.52 Td [(v)]TJ/F121 9.9626 Tf 9.864 6.165 Td [(\025)]TJ/F126 9.9626 Tf 10.28 0 Td [(v)]TJ/F121 9.9626 Tf 7.464 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 39.797 166.922 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -166.922 cm BT /F121 9.9626 Tf 73.67 145.005 Td [(D)]TJ/F34 9.9626 Tf 10.538 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.104 Td [(")]TJ/F117 7.5716 Tf 0 -8.435 Td [(1)]TJ/F151 9.9626 Tf 6.823 14.329 Td [(\020)]TJ/F123 9.9626 Tf 6.197 -10.998 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.096 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.283 Td [(\000)]TJ/F117 5.9776 Tf -0.985 -6.247 Td [(e)]TJ/F126 5.9776 Tf 2.654 1.728 Td [(v)]TJ/F121 9.9626 Tf 7.412 4.332 Td [(2)-278(T)]TJ/F117 9.9626 Tf 12.352 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 9.9626 Tf 4.489 -4.114 Td [(UI)]TJ/F126 9.9626 Tf 10.195 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.294 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.369 Td [(e)]TJ/F123 5.9776 Tf 3.361 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.105 0.887 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.28 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.189 Td [(v)]TJ/F151 9.9626 Tf 4.337 11.795 Td [(\021)]TJ ET 1 0 0 1 39.797 145.005 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -145.005 cm BT /F121 9.9626 Tf 73.67 117.214 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.923 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.749 Td [(v)]TJ/F121 7.5716 Tf 3.648 -2.749 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.749 Td [(v)]TJ/F121 5.9776 Tf 3.15 0 Td [(\000)]TJ/F126 5.9776 Tf 4.662 0 Td [(\022)]TJ/F117 7.5716 Tf -28.653 -22.342 Td [(0)]TJ/F126 9.9626 Tf 32.878 8.957 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.114 Td [(\000)]TJ/F123 9.9626 Tf 10.623 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F124 9.9626 Tf 9.1 -4.114 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(1)]TJ/F151 9.9626 Tf 5.944 12.496 Td [(\020)]TJ/F117 9.9626 Tf 5.43 -10.998 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.114 Td [(\000)]TJ/F123 9.9626 Tf 10.752 0 Td [(X)]TJ/F126 7.5716 Tf 6.805 -3.096 Td [(\033)]TJ/F121 5.9776 Tf 5.027 3.283 Td [(\000)]TJ/F117 5.9776 Tf -0.984 -6.247 Td [(e)]TJ/F126 5.9776 Tf 2.654 1.728 Td [(v)]TJ/F121 9.9626 Tf 7.412 4.332 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.618 0 Td [(y)]TJ/F121 9.9626 Tf 4.942 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.294 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.369 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.188 Td [(u)]TJ/F126 9.9626 Tf 7.104 0.887 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.154 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.279 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.188 Td [(v)]TJ/F151 9.9626 Tf 4.338 11.795 Td [(\021)]TJ ET 1 0 0 1 39.797 117.214 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -117.214 cm BT /F121 9.9626 Tf 73.67 86.836 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.922 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.748 Td [(v)]TJ/F121 7.5716 Tf 3.648 -2.748 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.748 Td [(v)]TJ/F121 5.9776 Tf 3.15 0 Td [(\000)]TJ/F126 5.9776 Tf 4.662 0 Td [(\022)]TJ/F117 7.5716 Tf -28.653 -22.341 Td [(0)]TJ/F126 9.9626 Tf 32.878 8.956 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.115 Td [(\000)]TJ/F123 9.9626 Tf 10.623 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F124 9.9626 Tf 9.1 -4.115 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(e)]TJ/F126 5.9776 Tf 3.362 2.188 Td [(v)]TJ/F151 9.9626 Tf 5.807 10.308 Td [(\020)]TJ/F121 9.9626 Tf 5.43 -10.999 Td [(\000)]TJ/F123 9.9626 Tf 8.538 0 Td [(X)]TJ/F126 7.5716 Tf 6.804 -3.095 Td [(\033)]TJ/F121 5.9776 Tf 5.028 3.282 Td [(\000)]TJ/F117 5.9776 Tf -0.985 -5.966 Td [(0)]TJ/F121 9.9626 Tf 9.411 5.779 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.618 0 Td [(y)]TJ/F121 9.9626 Tf 4.942 0 Td [(I)]TJ/F126 9.9626 Tf 5.217 0 Td [(\033)]TJ/F121 7.5716 Tf 6.615 4.295 Td [(C)]TJ/F126 7.5716 Tf -1.295 -7.663 Td [(.)]TJ/F117 7.5716 Tf 2.824 0 Td [(e)]TJ/F123 5.9776 Tf 3.362 2.188 Td [(u)]TJ/F121 7.5716 Tf 3.804 -2.188 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.188 Td [(v)]TJ/F126 7.5716 Tf 3.649 -2.188 Td [(/)]TJ/F126 9.9626 Tf 6.089 3.368 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.154 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.296 -7.625 Td [(0)]TJ/F151 9.9626 Tf 7.7 14.329 Td [(\021)]TJ ET 1 0 0 1 39.797 86.836 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -86.836 cm BT /F121 9.9626 Tf 73.67 60.01 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-100(\013)40(\032)]TJ ET q 1 0 0 1 85.404 62.501 cm []0 d 0 J 0.458 w 0 0 m 31.578 0 l S Q BT /F126 9.9626 Tf 97.706 52.937 Td [(\031)]TJ 20.471 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ ET 1 0 0 1 39.797 60.01 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -14.196 cm 0 g 0 G 1 0 0 1 382.565 0 cm 0 g 0 G endstream endobj 51 0 obj <> endobj 52 0 obj <> /Type /Annot /C [ 1 0 0 ] /Border [ 0 0 0 ] /Subtype /Link /Rect [ 239.684 297.528 251.639 308.472 ] >> endobj 53 0 obj <> /ProcSet [ /PDF /Text ] >> endobj 54 0 obj <>stream 1 0 0 1 45.354 629.624 cm 0 g 0 G 1 0 0 1 -45.354 -629.624 cm BT /F123 7.9701 Tf 92.53 629.624 Td [(L.)-250(Chaumont)-250(et)-250(al.)-250(/)-250(Stoc)15(hastic)-250(Pr)45(ocesses)-250(and)-250(their)-250(Applications)-250(119)-250(\0502009\051)-250(980\2261000)]TJ/F117 7.9701 Tf 323.435 0 Td [(987)]TJ ET 1 0 0 1 427.92 629.624 cm 0 g 0 G 1 0 0 1 -427.92 -629.624 cm BT /F121 9.9626 Tf 89.19 600.339 Td [(\002)]TJ/F151 9.9626 Tf 11.131 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.824 -2.922 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.748 Td [(v)]TJ/F121 7.5716 Tf 3.649 -2.748 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(e)]TJ/F126 5.9776 Tf 3.361 2.748 Td [(v)]TJ/F121 5.9776 Tf 3.15 0 Td [(\000)]TJ/F126 5.9776 Tf 4.663 0 Td [(\022)]TJ/F117 7.5716 Tf -28.653 -22.341 Td [(0)]TJ/F126 9.9626 Tf 32.877 8.956 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 9.9626 Tf 6.703 -4.115 Td [(\000)]TJ/F123 9.9626 Tf 10.622 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F126 7.5716 Tf 3.717 4.115 Td [(\013)40(\032)]TJ/F123 9.9626 Tf 9.737 -4.115 Td [(y)]TJ/F121 7.5716 Tf 4.941 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.115 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.9 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td 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Tf 57.31 555.637 Td [(Note)-220(that)-220(since)-220(the)-220(process)]TJ/F126 9.9626 Tf 107.8 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.089 5.105 Td [(")]TJ/F123 7.5716 Tf 0.204 -6.717 Td [(x)]TJ/F126 9.9626 Tf 4.958 1.612 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)]TJ/F123 9.9626 Tf 4.953 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0,)-220(is)-220(an)]TJ/F126 9.9626 Tf 30.101 0 Td [(\013)]TJ/F117 9.9626 Tf 6.087 0 Td [(-stable)-220(process)-220(conditioned)-220(to)-220(stay)-221(positi)26(v)14(e,)]TJ ET 1 0 0 1 45.354 555.637 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -555.637 cm BT /F117 9.9626 Tf 45.354 543.682 Td [(it)-254(follo)25(ws)-255(that,)-254(in)-254(the)-254(case)-255(that)-254(there)-254(are)-255(tw)10(o-sided)-254(jumps,)-254(there)-254(is)-255(no)-254(creeping)-254(out)-255(of)-254(the)-254(interv)25(al)]TJ ET 1 0 0 1 45.354 543.682 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -543.682 cm BT /F126 9.9626 Tf 45.354 531.727 Td [(.v)-40(;)]TJ/F123 9.9626 Tf 13.925 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(/)]TJ/F117 9.9626 Tf 6.207 0 Td [(with)-250(probability)-250(one.)-250(That)-250(is)-250(to)-250(say)65(,)]TJ ET 1 0 0 1 45.354 531.727 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -531.727 cm BT /F123 9.9626 Tf 70.141 509.712 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.439 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.865 6.255 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(u)]TJ/F121 9.9626 Tf 5.509 0 Td [(I)]TJ/F123 9.9626 Tf 5.447 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F123 9.9626 Tf 11.415 0 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 9.9626 Tf 9.865 6.165 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(v)]TJ/F121 9.9626 Tf 5.25 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.768 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.982 0 Td [(:)]TJ ET 1 0 0 1 45.354 509.712 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -509.712 cm BT /F117 9.9626 Tf 57.31 487.61 Td [(T)80(aking)]TJ/F126 9.9626 Tf 29.747 0 Td [(v)]TJ/F121 9.9626 Tf 8.017 0 Td [(#)-278(\0001)]TJ/F117 9.9626 Tf 29.168 0 Td [(in)-233(the)-233(\002rst)-233(part)-232(of)-233(the)-233(abo)15(v)15(e)-233(theorem)-233(and)]TJ/F123 9.9626 Tf 162.798 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(")-278(1)]TJ/F117 9.9626 Tf 21.396 0 Td [(in)-233(the)-233(second)-233(part)-233(we)-232(obtain)]TJ ET 1 0 0 1 45.354 487.61 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -487.61 cm BT /F117 9.9626 Tf 45.354 475.655 Td [(the)-250(solution)-250(to)-250(the)-250(one-sided)-250(e)15(xit)-250(problem)-250(as)-250(follo)25(ws.)]TJ ET 1 0 0 1 45.354 475.655 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.944 cm 0 g 0 G 1 0 0 1 -41.369 -452.711 cm BT /F124 9.9626 Tf 45.354 452.711 Td [(Cor)18(ollary)-250(1.)]TJ ET 1 0 0 1 96.642 452.711 cm 0 g 0 G 1 0 0 1 -96.642 -452.711 cm BT /F123 9.9626 Tf 100.627 452.711 Td [(F)45(ix)]TJ/F126 9.9626 Tf 15.352 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F123 9.9626 Tf 7.472 0 Td [(and)]TJ/F121 9.9626 Tf 17.704 0 Td [(\0001)]TJ/F126 9.9626 Tf 20.71 0 Td [(<)-278(v)-318(<)]TJ/F117 9.9626 Tf 29.094 0 Td [(0)]TJ/F126 9.9626 Tf 7.748 0 Td [(<)]TJ/F123 9.9626 Tf 10.539 0 Td [(u)]TJ/F126 9.9626 Tf 8.276 0 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F123 9.9626 Tf 10.172 0 Td [(.)]TJ ET 1 0 0 1 45.354 452.711 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -452.711 cm BT /F123 9.9626 Tf 70.141 431.391 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.998 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.998 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.034 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(C)]TJ/F123 5.9776 Tf -1.439 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.311 6.255 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)-87(;)]TJ/F123 9.9626 Tf 10.437 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 10.172 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 431.391 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -431.391 cm BT /F121 9.9626 Tf 79.227 407.102 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 409.593 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 400.028 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F117 9.9626 Tf 7.903 -4.114 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ ET 1 0 0 1 45.354 407.102 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -407.102 cm BT /F123 9.9626 Tf 45.354 385.224 Td [(and)]TJ ET 1 0 0 1 45.354 385.224 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -385.224 cm BT /F123 9.9626 Tf 70.141 366.429 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.465 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.52 Td [(v)]TJ/F121 9.9626 Tf 9.865 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 10.172 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 366.429 cm 0 g 0 G 0 g 0 G 1 0 0 1 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Tf 51.752 357.491 Td [(Finally)65(,)-340(to)-341(complete)-340(this)-340(subsection,)-340(when)]TJ/F126 9.9626 Tf 175.218 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(")]TJ/F117 7.5716 Tf 0 -8.435 Td [(1)]TJ/F126 9.9626 Tf 5.162 3.33 Td [(/)]TJ/F117 9.9626 Tf 7.106 0 Td [(is)-340(a)-340(spectrally)-341(ne)15(g)5(ati)25(v)15(e)-340(process)-340(we)-340(also)]TJ ET 1 0 0 1 39.797 357.491 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -357.491 cm BT /F117 9.9626 Tf 39.797 344.498 Td [(g)5(ain)-377(some)-377(information)-377(concerning)-377(the)-377(scale)-378(function,)]TJ/F123 9.9626 Tf 223.778 0 Td [(W)]TJ/F121 7.5716 Tf 9.574 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.616 Td [(,)-377(of)-377(the)-377(underlying)-378(L)]TJ 87.801 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-377(process,)]TJ ET 1 0 0 1 39.797 344.498 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -344.498 cm BT /F117 9.9626 Tf 39.797 332.543 Td [(denoted)-235(here)-235(by)]TJ/F126 9.9626 Tf 65.671 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.616 Td [(.)-235(Speci\002cally)65(,)-235(in)-235(that)-235(case)-235(it)-235(is)-235(kno)25(wn)-234(that)-235(1)]TJ/F121 9.9626 Tf 172.918 0 Td [(\000)]TJ/F126 9.9626 Tf 9.429 0 Td [(\032)]TJ/F121 9.9626 Tf 8.794 0 Td [(D)]TJ/F117 9.9626 Tf 10.539 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(=\013)]TJ/F117 9.9626 Tf 13.11 0 Td [(\050and)]TJ/F126 9.9626 Tf 20.044 0 Td [(\013)]TJ/F121 9.9626 Tf 8.855 0 Td [(2)]TJ/F126 9.9626 Tf 9.033 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(2)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(\051)-235(and)]TJ ET 1 0 0 1 39.797 332.543 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -332.543 cm BT /F117 9.9626 Tf 39.797 319.235 Td [(that)]TJ/F123 9.9626 Tf 18.549 0 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\030)]TJ ET q 1 0 0 1 76.737 315.748 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 82.077 322.887 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F121 7.5716 Tf -7.17 -8.205 Td [(1)]TJ/F121 9.9626 Tf 14.662 4.553 Td [(\024)]TJ/F123 9.9626 Tf 10.989 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.925 0 Td [(D)]TJ/F123 9.9626 Tf 10.979 0 Td [(m)-84(W)]TJ/F121 7.5716 Tf 17.604 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.616 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)-274(where)]TJ/F123 9.9626 Tf 32.287 0 Td [(m)]TJ/F121 9.9626 Tf 10.989 0 Td [(D)]TJ/F123 9.9626 Tf 11.667 0 Td [(E)]TJ/F126 9.9626 Tf 6.983 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.104 Td [(")]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ -8.266 -8.435 Td [(1)]TJ/F126 9.9626 Tf 12.55 3.331 Td [(/)]TJ/F117 9.9626 Tf 6.444 0 Td [(\050see)-274(for)-274(instance)-274(Theorem)-274(8.1)-273(in)-274([)]TJ ET 1 0 0 1 398.054 319.235 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -398.054 -319.235 cm BT /F117 9.9626 Tf 398.054 319.235 Td [(19)]TJ ET 1 0 0 1 408.017 319.235 cm 0 g 0 G 1 0 0 1 -408.017 -319.235 cm BT /F117 9.9626 Tf 408.017 319.235 Td [(])-274(or)]TJ ET 1 0 0 1 39.797 319.235 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -319.235 cm BT /F117 9.9626 Tf 39.797 307.279 Td [(identity)-250(\0509.4.3\051)-250(in)-250([)]TJ ET 1 0 0 1 115.343 307.279 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -115.343 -307.279 cm BT /F117 9.9626 Tf 115.343 307.279 Td [(15)]TJ ET 1 0 0 1 125.305 307.279 cm 0 g 0 G 1 0 0 1 -125.305 -307.279 cm BT /F117 9.9626 Tf 125.305 307.279 Td [(]\051.)-250(This)-250(implies)]TJ ET 1 0 0 1 39.797 307.279 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -307.279 cm BT /F123 9.9626 Tf 63.956 283.292 Td [(W)]TJ/F121 7.5716 Tf 9.574 4.115 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F117 9.9626 Tf 13.134 6.984 Td [(1)]TJ ET q 1 0 0 1 112.497 285.783 cm []0 d 0 J 0.458 w 0 0 m 7.781 0 l S Q BT /F123 9.9626 Tf 112.497 276.219 Td [(m)]TJ/F126 9.9626 Tf 8.976 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.111 0 Td [(x)]TJ/F126 9.9626 Tf 4.533 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.717 4.115 Td [(\013)40(\032)]TJ/F121 9.9626 Tf 11.866 -4.115 Td [(D)]TJ/F117 9.9626 Tf 13.134 6.984 Td [(1)]TJ ET q 1 0 0 1 184.753 285.783 cm []0 d 0 J 0.458 w 0 0 m 7.781 0 l S Q BT /F123 9.9626 Tf 184.753 276.219 Td [(m)]TJ/F126 9.9626 Tf 8.976 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.11 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(:)]TJ ET 1 0 0 1 39.797 283.292 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -283.292 cm BT /F117 9.9626 Tf 39.797 261.173 Td [(Recall)-235(that)-234(for)-235(a)-235(gi)25(v)15(en)-234(spectrally)-235(ne)15(g)5(ati)25(v)15(e)-235(L)]TJ 173.074 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-235(process)-234(it)-235(is)-235(kno)25(wn)-235(that)-234(the)-235(Laplace)-235(transform)-234(of)]TJ ET 1 0 0 1 39.797 261.173 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -261.173 cm BT /F117 9.9626 Tf 39.797 249.218 Td [(the)-327(scale)-327(function)-328(is)-327(gi)25(v)15(en)-327(by)-327(the)-327(in)40(v)15(erse)-328(of)-327(the)-327(associated)-327(Laplace)-328(e)15(xponent)-327(\050see)-327(for)-327(instance)]TJ ET 1 0 0 1 39.797 249.218 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -249.218 cm BT /F117 9.9626 Tf 39.797 237.263 Td [(Theorem)-444(VII.8)-443(in)-444(Bertoin)-443([)]TJ ET 1 0 0 1 155.694 237.263 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -155.694 -237.263 cm BT /F117 9.9626 Tf 155.694 237.263 Td [(2)]TJ ET 1 0 0 1 160.675 237.263 cm 0 g 0 G 1 0 0 1 -160.675 -237.263 cm BT /F117 9.9626 Tf 160.675 237.263 Td [(]\051.)-445(W)80(e)-443(can)-444(therefore)-443(compute)-444(the)-443(Laplace)-444(e)15(xponent)]TJ/F126 9.9626 Tf 221.694 0 Td [(\040)]TJ/F121 7.5716 Tf 7.91 3.617 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.617 Td [(.\022)-100(/)]TJ/F121 9.9626 Tf 19.15 0 Td [(D)]TJ ET 1 0 0 1 39.797 237.263 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -237.263 cm BT /F117 9.9626 Tf 39.797 222.372 Td [(log)]TJ/F123 9.9626 Tf 15.08 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.829 Td [(\022)-100(\030)]TJ/F121 5.9776 Tf 8.147 3.922 Td [(")]TJ/F126 5.9776 Tf 3.682 0 Td [(;)]TJ/F117 5.9776 Tf 1.979 0 Td [(n)]TJ -6.494 -6.606 Td [(1)]TJ/F126 9.9626 Tf 10.479 -1.145 Td [(/)]TJ/F117 9.9626 Tf 6.207 0 Td [(for)]TJ/F126 9.9626 Tf 14.107 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0,)-250(as)-250(follo)25(ws:)]TJ ET 1 0 0 1 39.797 222.372 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -222.372 cm BT /F126 9.9626 Tf 63.707 195.476 Td [(\040)]TJ/F121 7.5716 Tf 7.91 4.115 Td [(")]TJ/F126 9.9626 Tf 5.163 -4.115 Td [(.\022)-100(/)]TJ/F121 9.9626 Tf 16.299 0 Td [(D)]TJ/F123 9.9626 Tf 11.257 0 Td [(m)]TJ/F151 9.9626 Tf 9.442 13.988 Td [(\022)]TJ 6.724 -0.429 Td [(Z)]TJ/F121 7.5716 Tf 9.823 -2.922 Td [(1)]TJ/F117 7.5716 Tf -4.562 -19.593 Td [(0)]TJ/F117 9.9626 Tf 14.452 8.956 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F123 7.5716 Tf 4.293 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.11 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F123 9.9626 Tf 5.25 0 Td [(x)]TJ/F151 9.9626 Tf 5.311 13.988 Td [(\023)]TJ/F121 7.5716 Tf 6.724 -2.465 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET 1 0 0 1 39.797 195.476 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -195.476 cm BT /F121 9.9626 Tf 93.079 162.351 Td [(D)]TJ/F123 9.9626 Tf 11.257 0 Td [(m)]TJ/F151 9.9626 Tf 9.442 16.976 Td [(\040)]TJ 6.904 -3.417 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.923 Td [(1)]TJ -4.563 -19.593 Td [(0)]TJ/F123 9.9626 Tf 10.507 8.957 Td [(u)]TJ/F126 7.5716 Tf 5.51 4.114 Td [(\022)]TJ/F121 7.5716 Tf 4.088 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)]TJ/F121 7.5716 Tf 4.627 0 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F123 9.9626 Tf 4.982 0 Td [(u)]TJ/F151 9.9626 Tf 5.509 16.976 Td [(!)]TJ/F121 7.5716 Tf 6.904 -2.464 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 9.9626 Tf 7.051 -14.512 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(m)]TJ/F40 9.9626 Tf 10.381 6.984 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(C)]TJ/F126 9.9626 Tf 9.984 0 Td [(\013)-40(/)]TJ ET q 1 0 0 1 251.041 164.842 cm []0 d 0 J 0.458 w 0 0 m 41.48 0 l S Q BT /F40 9.9626 Tf 251.041 155.277 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)-100(/)]TJ/F40 9.9626 Tf 12.812 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(/)]TJ 14.715 7.074 Td [(:)]TJ ET 1 0 0 1 39.797 162.351 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -162.351 cm BT /F117 9.9626 Tf 51.752 134.97 Td [(Kno)25(wledge)-376(of)-376(the)-376(scale)-377(function)-376(allo)25(w)-376(us)-376(to)-376(write)-376(a)-376(stronger)-376(result)-377(than)-376(the)-376(one)-376(gi)25(v)15(en)-376(in)]TJ ET 1 0 0 1 39.797 134.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -11.956 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -39.797 -123.014 cm BT /F117 9.9626 Tf 39.797 123.014 Td [(Corollary)-250(1)]TJ ET 1 0 0 1 85.455 123.014 cm 0 g 0 G 1 0 0 1 -85.455 -123.014 cm BT /F117 9.9626 Tf 87.946 123.014 Td [(as)-250(follo)25(ws.)]TJ ET 1 0 0 1 39.797 123.014 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.245 cm 0 g 0 G 1 0 0 1 -35.812 -100.769 cm BT /F124 9.9626 Tf 39.797 100.769 Td [(Lemma)-250(2.)]TJ ET 1 0 0 1 82.407 100.769 cm 0 g 0 G 1 0 0 1 -82.407 -100.769 cm BT /F123 9.9626 Tf 86.392 100.769 Td [(Let)]TJ/F126 9.9626 Tf 15.402 0 Td [(\030)]TJ ET q 1 0 0 1 101.794 97.282 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 107.134 104.421 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -7.17 -8.205 Td [(t)]TJ/F121 9.9626 Tf 14.221 4.553 Td [(D)]TJ/F117 9.9626 Tf 10.539 0 Td [(inf)]TJ/F117 7.5716 Tf 11.068 -1.498 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.399 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(t)]TJ/F126 9.9626 Tf 4.945 1.498 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -8.266 -6.717 Td [(s)]TJ/F123 9.9626 Tf 12.55 1.612 Td [(.)-250(F)105(or)]TJ/F126 9.9626 Tf 21.599 0 Td [(v)-318(<)]TJ/F117 9.9626 Tf 18.556 0 Td [(0)]TJ/F123 9.9626 Tf 4.981 0 Td [(,)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)-167(\036)]TJ/F121 9.9626 Tf 13.972 0 Td [(\025)]TJ/F126 9.9626 Tf 10.279 0 Td [(\021)]TJ/F123 9.9626 Tf 7.871 0 Td [(and)]TJ/F126 9.9626 Tf 17.703 0 Td [(\021)]TJ/F121 9.9626 Tf 8.148 0 Td [(2)-278(T)]TJ/F117 9.9626 Tf 12.351 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F121 9.9626 Tf 4.958 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(v)]TJ/F121 9.9626 Tf 5.25 0 Td [(U)]TJ/F123 9.9626 Tf 5.809 0 Td [(we)-250(have)]TJ ET 1 0 0 1 39.797 100.769 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -100.769 cm BT /F123 9.9626 Tf 64.584 77.508 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.464 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -8.092 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.519 Td [(v)]TJ/F121 9.9626 Tf 11.228 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)-87(;)-167(\030)]TJ/F121 7.5716 Tf 15.548 5.105 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -8.092 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.519 Td [(v)]TJ/F121 7.5716 Tf 6.599 1.237 Td [(\000)]TJ/F121 9.9626 Tf 8.618 4.928 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(v)]TJ/F121 9.9626 Tf 8.018 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)-77(;)-167(\030)]TJ ET q 1 0 0 1 206.853 74.021 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 212.193 82.613 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -6.996 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 7.5716 Tf 6.6 1.237 Td [(\000)]TJ/F121 9.9626 Tf 8.617 4.928 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(v)]TJ/F121 9.9626 Tf 8.018 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)]TJ/F151 9.9626 Tf 5.38 10.999 Td [(\021)]TJ ET 1 0 0 1 39.797 77.508 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -77.508 cm BT /F121 9.9626 Tf 73.67 57.769 Td [(D)]TJ/F123 9.9626 Tf 11.146 0 Td [(K)]TJ/F121 7.5716 Tf 8.01 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 5.944 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\021)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(2)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\021)]TJ/F126 9.9626 Tf 4.586 -4.114 Td [(/.)]TJ/F117 9.9626 Tf 7.432 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 7.5716 Tf 4.088 0 Td [(\000)]TJ/F126 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Tf 4.424 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\021)]TJ/F126 9.9626 Tf 4.586 -4.115 Td [(/.)]TJ/F117 9.9626 Tf 7.433 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 7.5716 Tf 4.088 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\036)]TJ/F126 9.9626 Tf 5.246 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F126 9.9626 Tf 5.124 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 7.5716 Tf 4.089 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\036)]TJ/F126 9.9626 Tf 5.245 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F117 9.9626 Tf 5.124 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ/F117 9.9626 Tf 5.379 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\036)]TJ/F117 9.9626 Tf 6.246 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\021)]TJ ET 1 0 0 1 45.354 400.646 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -400.646 cm BT /F121 9.9626 Tf 81.369 370.735 Td [(D)]TJ/F117 9.9626 Tf 16.408 6.984 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.616 Td [(.\013)]TJ/F121 7.5716 Tf 7.45 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(2)]TJ/F126 7.5716 Tf 3.786 0 Td [(/v)]TJ ET q 1 0 0 1 93.823 373.226 cm []0 d 0 J 0.458 w 0 0 m 36.786 0 l S Q BT /F126 9.9626 Tf 93.823 363.661 Td [(\013)-40(.\013)]TJ/F121 9.9626 Tf 18.104 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F151 9.9626 Tf 6.572 20.633 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.923 Td [(e)]TJ/F121 5.9776 Tf 3.362 2.749 Td [(\000)]TJ/F126 5.9776 Tf 4.662 0 Td [(v)]TJ/F117 7.5716 Tf -12.587 -22.342 Td [(1)]TJ/F126 9.9626 Tf 24.869 15.941 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 3.616 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(v)]TJ/F121 9.9626 Tf 6.702 -3.616 Td [(\000)]TJ/F123 9.9626 Tf 10.623 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ ET q 1 0 0 1 158.315 373.226 cm []0 d 0 J 0.458 w 0 0 m 50.586 0 l S Q BT /F123 9.9626 Tf 158.952 363.579 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(.)]TJ/F123 9.9626 Tf 4.353 0 Td [(y)]TJ/F121 9.9626 Tf 7.156 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 2.879 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 5.479 4.277 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 7.155 0 Td [(\000)]TJ/F126 9.9626 Tf 11.181 6.984 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.616 Td [(v)]TJ/F126 9.9626 Tf 4.488 -3.616 Td [(/)]TJ/F126 7.5716 Tf 3.716 3.616 Td [(\013)]TJ/F121 7.5716 Tf 4.627 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET q 1 0 0 1 234.051 373.226 cm []0 d 0 J 0.458 w 0 0 m 48.34 0 l S Q BT /F126 9.9626 Tf 239.827 363.661 Td [(\013)-40(.\013)]TJ/F121 9.9626 Tf 18.105 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ 33.737 14.058 Td [(\031)]TJ ET q 1 0 0 1 284.781 373.226 cm []0 d 0 J 0.458 w 0 0 m 50.681 0 l S Q BT /F117 9.9626 Tf 284.781 363.661 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-72(.\013)]TJ/F121 9.9626 Tf 18.712 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ ET 1 0 0 1 45.354 370.735 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -370.735 cm BT /F117 9.9626 Tf 45.354 346.856 Td [(and)-250(the)-250(proof)-250(is)-250(complete.)]TJ/F116 9.9626 Tf 116.214 0 Td [(\004)]TJ ET 1 0 0 1 45.354 346.856 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -346.856 cm BT /F123 9.9626 Tf 45.354 320.952 Td [(3.2.)-500(Calculations)-250(for)]TJ/F126 9.9626 Tf 87.461 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(\003)]TJ ET 1 0 0 1 45.354 320.952 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -320.952 cm BT /F117 9.9626 Tf 57.31 295.212 Td [(Henceforth)-390(we)-391(shall)-390(assume)-391(that)]TJ/F126 9.9626 Tf 138.97 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(/)]TJ/F117 9.9626 Tf 7.606 0 Td [(is)-390(an)]TJ/F126 9.9626 Tf 23.829 0 Td [(\013)]TJ/F117 9.9626 Tf 6.088 0 Td [(-stable)-390(process)-391(killed)-390(on)-391(\002rst)-390(e)15(xit)-391(of)-390(the)]TJ ET 1 0 0 1 45.354 295.212 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -295.212 cm BT /F117 9.9626 Tf 45.354 283.257 Td [(positi)25(v)15(e)-290(half-line)-289(starting)-290(from)]TJ/F123 9.9626 Tf 125.968 0 Td [(x)]TJ/F126 9.9626 Tf 8.807 0 Td [(>)]TJ/F117 9.9626 Tf 11.268 0 Td [(0.)-290(As)-289(before,)-290(unless)-289(otherwise)-290(stated,)-290(we)-289(shall)-290(assume)-289(that)]TJ ET 1 0 0 1 45.354 283.257 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -283.257 cm BT /F117 9.9626 Tf 45.354 271.302 Td [(there)-263(are)-263(tw)10(o-sided)-262(jumps,)-263(moreo)15(v)15(er)40(,)-263(spectrally)-263(one-sided)-262(results)-263(may)-263(be)-263(considered)-262(as)-263(limiting)]TJ ET 1 0 0 1 45.354 271.302 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -271.302 cm BT /F117 9.9626 Tf 45.354 259.347 Td [(cases)-281(of)-281(the)-280(tw)10(o-sided)-281(jumps)-281(case.)-281(W)80(e)-281(start)-281(with)-281(the)-280(tw)10(o-)-281(and)-281(one-sided)-281(e)15(xit)-281(problems)-280(with)-281(the)]TJ ET 1 0 0 1 45.354 259.347 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -259.347 cm BT /F117 9.9626 Tf 45.354 247.392 Td [(latter)-313(as)-313(a)-313(limiting)-312(case)-313(of)-313(the)-313(former)55(.)-313(W)80(e)-313(of)25(fer)-313(no)-313(proof)-313(as)-313(the)-313(calculations)-312(are)-313(essentially)-313(the)]TJ ET 1 0 0 1 45.354 247.392 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -247.392 cm BT /F117 9.9626 Tf 45.354 235.437 Td [(same.)]TJ ET 1 0 0 1 45.354 235.437 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -20.982 cm 0 g 0 G 1 0 0 1 -41.369 -214.455 cm BT /F124 9.9626 Tf 45.354 214.455 Td [(Theor)18(em)-250(3.)]TJ ET 1 0 0 1 93.872 214.455 cm 0 g 0 G 1 0 0 1 -93.872 -214.455 cm BT /F123 9.9626 Tf 97.857 214.455 Td [(F)45(ix)]TJ/F126 9.9626 Tf 15.352 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.28 0 Td [(0)]TJ/F123 9.9626 Tf 7.472 0 Td [(and)]TJ/F121 9.9626 Tf 17.703 0 Td [(\0001)]TJ/F126 9.9626 Tf 20.71 0 Td [(<)-278(v)-318(<)]TJ/F117 9.9626 Tf 29.094 0 Td [(0)]TJ/F126 9.9626 Tf 7.749 0 Td [(<)]TJ/F123 9.9626 Tf 10.538 0 Td [(u)]TJ/F126 9.9626 Tf 8.277 0 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F123 9.9626 Tf 10.172 0 Td [(.)]TJ ET 1 0 0 1 45.354 214.455 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -214.455 cm BT /F123 9.9626 Tf 70.141 193.747 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 4.115 Td [(\003)]TJ/F123 7.5716 Tf -0.921 -8.595 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(C)]TJ/F123 5.9776 Tf -1.439 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.311 5.806 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 45.354 193.747 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -193.747 cm BT /F121 9.9626 Tf 79.227 169.458 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 171.949 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 162.385 Td [(\031)]TJ 33.176 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ ET 1 0 0 1 45.354 169.458 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -169.458 cm BT /F121 9.9626 Tf 89.19 148.934 Td [(\002)]TJ/F126 9.9626 Tf 9.471 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 7.5716 Tf 4.188 0 Td [(C)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/.)]TJ/F117 9.9626 Tf 7.432 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.115 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.8 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F126 9.9626 Tf 4.686 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ ET 1 0 0 1 45.354 148.934 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -148.934 cm BT /F123 9.9626 Tf 45.354 130.06 Td [(and)]TJ ET 1 0 0 1 45.354 130.06 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -130.06 cm BT /F123 9.9626 Tf 70.141 111.185 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.465 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 4.115 Td [(\003)]TJ/F123 7.5716 Tf -0.921 -8.595 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.52 Td [(v)]TJ/F121 9.9626 Tf 9.865 5.717 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 45.354 111.185 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -111.185 cm BT /F121 9.9626 Tf 79.227 86.946 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)40(\032)]TJ ET q 1 0 0 1 90.961 89.437 cm []0 d 0 J 0.458 w 0 0 m 31.578 0 l S Q BT /F126 9.9626 Tf 103.263 79.873 Td [(\031)]TJ 20.471 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\032)-60(/)]TJ ET 1 0 0 1 45.354 86.946 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -86.946 cm BT /F121 9.9626 Tf 89.19 66.422 Td [(\002)]TJ/F126 9.9626 Tf 9.471 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.114 Td [(/.)]TJ/F117 9.9626 Tf 7.432 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td 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G 1 0 0 1 -39.797 -543.093 cm BT /F123 9.9626 Tf 64.584 525.179 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.998 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.998 Td [(v)]TJ/F121 9.9626 Tf 7.464 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 4.114 Td [(\003)]TJ/F123 7.5716 Tf -0.922 -8.594 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.519 Td [(v)]TJ/F121 9.9626 Tf 9.864 5.717 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.114 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.794 Td [(v)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 10.172 10.998 Td [(\021)]TJ ET 1 0 0 1 39.797 525.179 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -525.179 cm BT /F121 9.9626 Tf 73.67 500.94 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.983 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-100(\013)40(\032)]TJ ET q 1 0 0 1 85.404 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459.39 Td [(\030)]TJ ET q 1 0 0 1 39.797 455.903 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 45.137 463.043 Td [(\003)]TJ 0 -8.206 Td [(1)]TJ/F117 9.9626 Tf 8.229 4.553 Td [(,)-399(of)]TJ/F126 9.9626 Tf 18.747 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F117 9.9626 Tf 8.421 -3.616 Td [(in)-399(a)-400(similar)-399(w)10(ay)-399(to)-400(the)-399(pre)25(vious)-399(section)-400(by)-399(inte)15(grating)-399(out)]TJ/F123 9.9626 Tf 248.034 0 Td [(u)]TJ/F117 9.9626 Tf 9.487 0 Td [(and)]TJ/F126 9.9626 Tf 18.365 0 Td [(v)]TJ/F117 9.9626 Tf 9.229 0 Td [(in)-399(the)-400(abo)15(v)15(e)]TJ ET 1 0 0 1 39.797 459.39 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -459.39 cm BT /F117 9.9626 Tf 39.797 447.435 Td [(corollary)65(.)-489(The)-488(la)15(w)-488(of)-488(the)-488(minimum)-487(w)10(as)-488(already)-488(computed)-488(in)-488([)]TJ ET 1 0 0 1 310.249 447.435 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -310.249 -447.435 cm BT /F117 9.9626 Tf 310.249 447.435 Td [(9)]TJ ET 1 0 0 1 315.231 447.435 cm 0 g 0 G 1 0 0 1 -315.231 -447.435 cm BT /F117 9.9626 Tf 315.231 447.435 Td [(,)]TJ ET 1 0 0 1 317.721 447.435 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -317.721 -447.435 cm BT /F117 9.9626 Tf 317.721 447.435 Td [(10)]TJ ET 1 0 0 1 327.684 447.435 cm 0 g 0 G 1 0 0 1 -327.684 -447.435 cm BT /F117 9.9626 Tf 327.684 447.435 Td [(])-488(and)-488(we)-488(refrain)-487(from)]TJ ET 1 0 0 1 39.797 447.435 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -447.435 cm BT /F117 9.9626 Tf 39.797 435.48 Td [(producing)-320(the)-319(alternati)25(v)15(e)-320(computations)-320(here.)-320(F)15(or)-319(the)-320(maximum,)-320(an)-319(easier)-320(approach)-320(is)-319(at)-320(hand.)]TJ ET 1 0 0 1 39.797 435.48 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -435.48 cm BT /F117 9.9626 Tf 39.797 423.525 Td [(Since)]TJ/F126 9.9626 Tf 24.207 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F117 9.9626 Tf 6.513 -3.616 Td 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[(\003)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 8.229 2.68 Td [(g)-278(\024)]TJ/F117 9.9626 Tf 16.732 0 Td [(e)]TJ/F123 7.5716 Tf 4.56 4.115 Td [(z)]TJ/F151 9.9626 Tf 3.807 6.884 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F124 9.9626 Tf 10.538 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.\033)]TJ/F121 7.5716 Tf 10.331 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.37 Td [(e)]TJ/F123 5.9776 Tf 3.47 2.188 Td [(z)]TJ/F126 9.9626 Tf 6.997 0.887 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.626 Td [(0)]TJ/F126 9.9626 Tf 7.699 3.331 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F124 9.9626 Tf 10.539 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -2.001 Td [(e)]TJ/F121 5.9776 Tf 3.362 2.188 Td [(\000)]TJ/F123 5.9776 Tf 4.77 0 Td [(z)]TJ/F126 9.9626 Tf 3.608 -0.187 Td [(.\033)]TJ/F121 7.5716 Tf 10.331 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.295 -7.626 Td [(1)]TJ/F126 9.9626 Tf 10.467 3.331 Td [(>)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.626 Td [(0)]TJ/F126 9.9626 Tf 7.699 3.331 Td [(/:)]TJ ET 1 0 0 1 39.797 401.959 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -401.959 cm BT /F117 9.9626 Tf 39.797 380.737 Td [(The)-267(probability)-268(on)-267(the)-268(right-hand)-267(side)-268(abo)15(v)15(e)-267(may)-268(be)-267(obtained)-268(from)]TJ ET 1 0 0 1 311.748 380.737 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -311.748 -380.737 cm BT /F117 9.9626 Tf 311.748 380.737 Td [(Theorem)-268(1)]TJ ET 1 0 0 1 355.36 380.737 cm 0 g 0 G 1 0 0 1 -355.36 -380.737 cm BT /F117 9.9626 Tf 358.024 380.737 Td [(by)-268(a)-267(straightfor)20(-)]TJ ET 1 0 0 1 39.797 380.737 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -380.737 cm BT /F117 9.9626 Tf 39.797 368.782 Td [(w)10(ard)-220(inte)15(gration.)-220(The)-220(latter)-220(calculation)-220(has)-221(already)-220(been)-220(performed)-220(ho)25(we)25(v)15(er)-220(in)-220(Rogozin)-220([)]TJ ET 1 0 0 1 392.503 368.782 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -392.503 -368.782 cm BT /F117 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257.496 306.046 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -257.496 -306.046 cm BT /F117 9.9626 Tf 257.496 306.046 Td [(9)]TJ ET 1 0 0 1 262.477 306.046 cm 0 g 0 G 1 0 0 1 -262.477 -306.046 cm BT /F117 9.9626 Tf 262.477 306.046 Td [(,)]TJ ET 1 0 0 1 264.968 306.046 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -264.968 -306.046 cm BT /F117 9.9626 Tf 264.968 306.046 Td [(10)]TJ ET 1 0 0 1 274.93 306.046 cm 0 g 0 G 1 0 0 1 -274.93 -306.046 cm BT /F117 9.9626 Tf 274.93 306.046 Td [(])-222(which)-221(we)-222(include)-221(for)-222(completeness,)]TJ ET 1 0 0 1 39.797 306.046 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -306.046 cm BT /F117 9.9626 Tf 39.797 294.091 Td [(we)-250(ha)20(v)15(e)-250(the)-250(follo)25(wing)-250(corollary)65(.)]TJ ET 1 0 0 1 39.797 294.091 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.045 cm 0 g 0 G 1 0 0 1 -35.812 -272.046 cm BT /F124 9.9626 Tf 39.797 272.046 Td [(Cor)18(ollary)-250(4.)]TJ ET 1 0 0 1 91.084 272.046 cm 0 g 0 G 1 0 0 1 -91.084 -272.046 cm BT /F123 9.9626 Tf 95.069 272.046 Td [(F)105(or)-291(z)]TJ/F121 9.9626 Tf 23.918 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F123 9.9626 Tf 7.472 0 Td [(we)-250(have)-250(that)]TJ ET 1 0 0 1 39.797 272.046 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -272.046 cm BT /F123 9.9626 Tf 64.584 249.235 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ ET q 1 0 0 1 78.578 257.414 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 78.578 249.235 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(\003)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 10.996 2.68 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.161 0 Td [(z)]TJ/F151 9.9626 Tf 4.353 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F40 9.9626 Tf 40.215 6.984 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.\013)-40(/)]TJ ET q 1 0 0 1 133.393 251.726 cm []0 d 0 J 0.458 w 0 0 m 78.057 0 l S Q BT /F40 9.9626 Tf 133.393 242.162 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)40(\032)-60(/)]TJ/F40 9.9626 Tf 18.75 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(.)]TJ/F117 9.9626 Tf 13.519 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\032)-60(//)]TJ 14.655 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.042 0 Td [(z)]TJ/F126 9.9626 Tf 3.807 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.042 0 Td [(z)]TJ/F126 9.9626 Tf 3.807 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F121 7.5716 Tf 8.602 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.283 -4.115 Td [(d)]TJ/F123 9.9626 Tf 5.161 0 Td [(z)]TJ ET 1 0 0 1 39.797 249.235 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -249.235 cm BT /F123 9.9626 Tf 39.797 226.504 Td [(and)]TJ ET 1 0 0 1 39.797 226.504 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -226.504 cm BT /F123 9.9626 Tf 64.584 205.626 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F121 9.9626 Tf 5.43 -10.999 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\030)]TJ ET q 1 0 0 1 86.349 202.139 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 91.689 209.74 Td [(\003)]TJ 0 -8.667 Td [(1)]TJ/F121 9.9626 Tf 10.996 4.553 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.16 0 Td [(z)]TJ/F151 9.9626 Tf 4.354 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F117 9.9626 Tf 44.157 6.984 Td [(1)]TJ ET q 1 0 0 1 141.164 208.117 cm []0 d 0 J 0.458 w 0 0 m 69.828 0 l S Q BT /F40 9.9626 Tf 141.164 198.552 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)40(\032)-60(/)]TJ/F40 9.9626 Tf 18.75 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td 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0 1 39.797 117.742 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -117.742 cm BT /F117 9.9626 Tf 51.752 93.634 Td [(Henceforth)-455(we)-454(shall)-455(assume)-455(that)]TJ/F126 9.9626 Tf 142.172 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.089 5.105 Td [(#)]TJ/F123 7.5716 Tf 0.204 -6.717 Td [(x)]TJ/F126 9.9626 Tf 4.958 1.612 Td [(/)]TJ/F117 9.9626 Tf 8.246 0 Td [(is)-455(an)]TJ/F126 9.9626 Tf 25.11 0 Td [(\013)]TJ/F117 9.9626 Tf 6.088 0 Td [(-stable)-455(process)-454(conditioned)-455(to)-455(hit)-454(zero)]TJ ET 1 0 0 1 39.797 93.634 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -93.634 cm BT /F117 9.9626 Tf 39.797 81.679 Td [(continuously)-345(start)1(ing)-345(from)]TJ/F123 9.9626 Tf 111.298 0 Td [(x)]TJ/F126 9.9626 Tf 9.823 0 Td [(>)]TJ/F117 9.9626 Tf 12.283 0 Td [(0.)-345(Ag)5(ain,)-345(unless)-344(otherwise)-345(stated,)-344(we)-345(shall)-345(assume)-344(that)-345(there)]TJ ET 1 0 0 1 39.797 81.679 cm 0 g 0 G 0 g 0 G 1 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629.624 cm 0 g 0 G 1 0 0 1 -45.354 -629.624 cm BT /F123 7.9701 Tf 92.53 629.624 Td [(L.)-250(Chaumont)-250(et)-250(al.)-250(/)-250(Stoc)15(hastic)-250(Pr)45(ocesses)-250(and)-250(their)-250(Applications)-250(119)-250(\0502009\051)-250(980\2261000)]TJ/F117 7.9701 Tf 323.435 0 Td [(991)]TJ ET 1 0 0 1 427.92 629.624 cm 0 g 0 G 1 0 0 1 -427.92 -629.624 cm BT /F117 9.9626 Tf 45.354 607.707 Td [(the)-240(tw)10(o-)-241(and)-240(one-sided)-240(e)15(xit)-241(problems)-240(without)-240(of)25(fering)-241(proofs)-240(since)-240(the)15(y)-241(follo)25(w)-240(in)-241(a)-240(similar)-240(spirit)]TJ ET 1 0 0 1 45.354 607.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -607.707 cm BT /F117 9.9626 Tf 45.354 595.751 Td [(to)-250(the)-250(calculations)-250(for)]TJ/F126 9.9626 Tf 89.095 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F117 9.9626 Tf 7.653 -3.617 Td [(and)]TJ ET 1 0 0 1 164.319 595.751 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -164.319 -595.751 cm BT /F117 9.9626 Tf 164.319 595.751 Td 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[(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 45.354 555.858 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -555.858 cm BT /F121 9.9626 Tf 79.227 531.569 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 534.06 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 524.496 Td [(\031)]TJ 33.176 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ ET 1 0 0 1 45.354 531.569 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -531.569 cm BT /F121 9.9626 Tf 89.19 511.045 Td [(\002)]TJ/F126 9.9626 Tf 9.471 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.188 0 Td [(C)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.188 0 Td [(C)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.717 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ ET 1 0 0 1 45.354 511.045 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -511.045 cm BT /F123 9.9626 Tf 45.354 493.764 Td [(and)]TJ ET 1 0 0 1 45.354 493.764 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -493.764 cm BT /F123 9.9626 Tf 70.141 476.482 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.465 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(#)]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.52 Td [(v)]TJ/F121 9.9626 Tf 9.865 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.795 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(>)]TJ/F123 9.9626 Tf 10.767 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F151 9.9626 Tf 8.297 13.679 Td [(\021)]TJ ET 1 0 0 1 45.354 476.482 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -476.482 cm BT /F121 9.9626 Tf 79.227 452.194 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.983 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 454.684 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 445.12 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.114 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)40(\032)]TJ ET 1 0 0 1 45.354 452.194 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -452.194 cm BT /F121 9.9626 Tf 89.19 431.669 Td [(\002)]TJ/F126 9.9626 Tf 9.471 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)-87(:)]TJ ET 1 0 0 1 45.354 431.669 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -25.681 cm 0 g 0 G 1 0 0 1 -41.369 -405.988 cm BT /F124 9.9626 Tf 45.354 405.988 Td [(Cor)18(ollary)-250(5.)]TJ ET 1 0 0 1 96.642 405.988 cm 0 g 0 G 1 0 0 1 -96.642 -405.988 cm BT /F123 9.9626 Tf 100.627 405.988 Td [(F)45(ix)]TJ/F126 9.9626 Tf 15.352 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F123 9.9626 Tf 4.982 0 Td [(.)]TJ ET 1 0 0 1 45.354 405.988 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -405.988 cm BT /F123 9.9626 Tf 70.141 386.181 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.439 -4.609 Td [(u)]TJ/F121 9.9626 Tf 9.311 6.255 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.114 Td [(C)]TJ/F123 7.5716 Tf -1.893 -6.794 Td [(u)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 10.172 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 386.181 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -386.181 cm BT /F121 9.9626 Tf 79.227 361.892 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET q 1 0 0 1 90.961 364.383 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F126 9.9626 Tf 115.968 354.818 Td [(\031)]TJ 33.176 7.074 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 9.9626 Tf 6.899 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.424 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.8 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F126 9.9626 Tf 4.686 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.114 Td [(u)]TJ/F121 7.5716 Tf 4.187 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 9.9626 Tf 6.801 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ ET 1 0 0 1 45.354 361.892 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -361.892 cm BT /F123 9.9626 Tf 45.354 341.527 Td [(and)]TJ ET 1 0 0 1 45.354 341.527 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -341.527 cm BT /F123 9.9626 Tf 70.141 324.246 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.465 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(")]TJ/F123 7.5716 Tf -0.921 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 9.9626 Tf 9.865 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 5.38 0 Td [(I)]TJ/F123 9.9626 Tf 5.446 0 Td [(T)]TJ/F121 7.5716 Tf 7.044 4.115 Td [(\000)]TJ/F126 7.5716 Tf -1.893 -6.795 Td [(v)]TJ/F126 9.9626 Tf 11.064 2.68 Td [(<)]TJ/F121 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 10.172 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 324.246 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -324.246 cm BT /F121 9.9626 Tf 79.227 300.007 Td [(D)]TJ/F117 9.9626 Tf 11.734 6.984 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)40(\032)]TJ ET q 1 0 0 1 90.961 302.498 cm []0 d 0 J 0.458 w 0 0 m 31.578 0 l S Q BT /F126 9.9626 Tf 103.263 292.934 Td [(\031)]TJ 20.471 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.488 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.1 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F121 9.9626 Tf 6.702 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)40(\032)]TJ/F126 9.9626 Tf 9.099 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F126 7.5716 Tf 4.424 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.99 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.586 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.717 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)-87(:)]TJ ET 1 0 0 1 45.354 300.007 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -300.007 cm BT /F117 9.9626 Tf 57.31 273.284 Td [(From)-266(the)-266(abo)15(v)15(e)-265(corollary)-266(we)-266(proceed)-266(to)-266(obtain)-265(the)-266(la)15(w)-266(of)-266(the)-266(maximum)-266(of)]TJ/F126 9.9626 Tf 301.691 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F117 9.9626 Tf 7.811 -3.616 Td [(\050recalling)-266(that)]TJ ET 1 0 0 1 45.354 273.284 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -273.284 cm BT /F117 9.9626 Tf 45.354 261.328 Td [(it)-250(is)-250(a)-250(process)-250(with)-250(drift)-250(to)]TJ/F121 9.9626 Tf 106.539 0 Td [(\0001)]TJ/F117 9.9626 Tf 17.943 0 Td [(\051.)]TJ ET 1 0 0 1 45.354 261.328 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -20.779 cm 0 g 0 G 1 0 0 1 -41.369 -240.549 cm BT /F124 9.9626 Tf 45.354 240.549 Td [(Cor)18(ollary)-250(6.)]TJ ET 1 0 0 1 96.642 240.549 cm 0 g 0 G 1 0 0 1 -96.642 -240.549 cm BT /F123 9.9626 Tf 100.627 240.549 Td [(F)105(or)-291(z)]TJ/F121 9.9626 Tf 23.918 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ ET 1 0 0 1 45.354 240.549 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -240.549 cm BT /F123 9.9626 Tf 70.141 220.743 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.998 Td [(\020)]TJ ET q 1 0 0 1 84.135 228.922 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 84.135 220.743 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 10.997 2.68 Td [(\024)]TJ/F123 9.9626 Tf 10.458 0 Td [(z)]TJ/F151 9.9626 Tf 4.354 10.998 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.998 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.114 Td [(\000)]TJ/F123 7.5716 Tf 6.042 0 Td [(z)]TJ/F126 9.9626 Tf 3.807 -4.114 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.114 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(1)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.114 Td [(:)]TJ ET 1 0 0 1 45.354 220.743 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -25.333 cm 0 g 0 G 1 0 0 1 -41.369 -195.41 cm BT /F124 9.9626 Tf 45.354 195.41 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 71.307 195.41 cm 0 g 0 G 1 0 0 1 -71.307 -195.41 cm BT /F117 9.9626 Tf 75.292 195.41 Td [(Similarly)-250(to)-250(the)-250(calculations)-250(in)-250(Section)]TJ ET 1 0 0 1 232.48 195.41 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -232.48 -195.41 cm BT /F117 9.9626 Tf 232.48 195.41 Td [(3.1)]TJ ET 1 0 0 1 244.934 195.41 cm 0 g 0 G 1 0 0 1 -244.934 -195.41 cm BT /F117 9.9626 Tf 247.424 195.41 Td [(we)-250(mak)10(e)-250(use)-250(of)-250(the)-250(f)10(act)-250(that)]TJ ET 1 0 0 1 45.354 195.41 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -195.41 cm BT /F123 9.9626 Tf 70.141 175.473 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ ET q 1 0 0 1 84.135 183.653 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 84.135 175.473 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 10.997 2.68 Td [(\024)]TJ/F123 9.9626 Tf 10.458 0 Td [(z)]TJ/F151 9.9626 Tf 4.354 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F123 9.9626 Tf 11.415 0 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F123 9.9626 Tf 3.945 0 Td [(T)]TJ/F121 7.5716 Tf 7.043 4.115 Td [(C)]TJ/F123 7.5716 Tf -1.756 -6.795 Td [(z)]TJ/F121 9.9626 Tf 10.928 2.68 Td [(D)-278(1)]TJ/F126 9.9626 Tf 20.71 0 Td [(/:)]TJ ET 1 0 0 1 45.354 175.473 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -175.473 cm BT /F117 9.9626 Tf 45.354 156.02 Td [(Hence)]TJ ET 1 0 0 1 45.354 156.02 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -156.02 cm BT /F123 9.9626 Tf 70.141 138.739 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ ET q 1 0 0 1 84.135 146.918 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 84.135 138.739 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 10.997 2.68 Td [(\024)]TJ/F123 9.9626 Tf 10.458 0 Td [(z)]TJ/F151 9.9626 Tf 4.354 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 138.739 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -138.739 cm BT /F121 9.9626 Tf 79.227 114.106 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 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Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F126 9.9626 Tf 7.903 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F123 7.5716 Tf 4.56 4.115 Td [(z)]TJ/F121 9.9626 Tf 6.021 -4.115 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ ET 1 0 0 1 39.797 573.144 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -573.144 cm BT /F121 9.9626 Tf 73.67 548.73 Td [(D)-278(T)]TJ/F126 9.9626 Tf 13.856 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.114 Td [(\000)]TJ/F123 7.5716 Tf 6.042 0 Td [(z)]TJ/F126 9.9626 Tf 3.807 -4.114 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.114 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F121 9.9626 Tf 10.117 -4.114 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 4.981 0 Td [(U)]TJ/F126 9.9626 Tf 29.52 6.983 Td [(\031)]TJ ET q 1 0 0 1 179.054 551.22 cm []0 d 0 J 0.458 w 0 0 m 56.987 0 l S Q BT /F117 9.9626 Tf 179.054 541.656 Td [(sin)]TJ/F126 9.9626 Tf 13.287 0 Td [(\031)-100(\013)-40(.)]TJ/F117 9.9626 Tf 16.777 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\032)-60(/)]TJ ET 1 0 0 1 39.797 548.73 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -548.73 cm BT /F117 9.9626 Tf 39.797 526.701 Td [(and)-250(hence)]TJ ET 1 0 0 1 39.797 526.701 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -526.701 cm BT /F123 9.9626 Tf 64.584 509.464 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ ET q 1 0 0 1 78.578 517.643 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 78.578 509.464 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ 0 -8.624 Td [(1)]TJ/F121 9.9626 Tf 10.996 2.68 Td [(\024)]TJ/F123 9.9626 Tf 10.459 0 Td [(z)]TJ/F151 9.9626 Tf 4.353 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.042 0 Td [(z)]TJ/F126 9.9626 Tf 3.807 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ ET 1 0 0 1 39.797 509.464 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -509.464 cm BT /F117 9.9626 Tf 39.797 489.916 Td [(as)-250(required.)]TJ/F116 9.9626 Tf 58.928 0 Td [(\004)]TJ ET 1 0 0 1 39.797 489.916 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -489.916 cm BT /F117 9.9626 Tf 51.752 472.196 Td [(No)25(w)65(,)-304(we)-304(suppose)-304(that)]TJ/F126 9.9626 Tf 91.741 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(#)]TJ/F117 7.5716 Tf 0 -8.435 Td [(1)]TJ/F126 9.9626 Tf 5.163 3.33 Td [(/)]TJ/F117 9.9626 Tf 6.746 0 Td [(has)-304(only)-304(positi)25(v)15(e)-304(jumps,)-304(in)-305(which)-304(case)]TJ/F126 9.9626 Tf 159.45 0 Td [(\032)]TJ/F121 9.9626 Tf 9.793 0 Td [(D)]TJ/F117 9.9626 Tf 11.537 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(=\013)]TJ/F117 9.9626 Tf 10.769 0 Td [(.)-304(W)80(e)-305(denote)]TJ ET 1 0 0 1 39.797 472.196 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -472.196 cm BT /F117 9.9626 Tf 39.797 459.203 Td [(by)]TJ/F126 9.9626 Tf 12.514 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F117 9.9626 Tf 6.835 -3.616 Td [(its)-256(underlying)-256(L)]TJ 64.324 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-256(process)-256(in)-256(this)-256(particular)-256(case.)-256(The)-256(associated)-256(scale)-256(function)-256(of)]TJ/F126 9.9626 Tf 270.141 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ ET 1 0 0 1 39.797 459.203 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -459.203 cm BT /F117 9.9626 Tf 39.797 447.248 Td [(can)-250(be)-250(identi\002ed)-250(as)]TJ ET 1 0 0 1 39.797 447.248 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -447.248 cm BT /F123 9.9626 Tf 64.395 426.409 Td [(E)]TJ/F126 9.9626 Tf 6.983 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.306 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(p)]TJ -8.267 -8.636 Td [(1)]TJ/F126 9.9626 Tf 12.55 3.33 Td [(/)]TJ/F123 9.9626 Tf 3.966 0 Td [(W)]TJ/F121 7.5716 Tf 9.574 4.115 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 11.415 0 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ ET q 1 0 0 1 165.841 434.589 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 165.841 426.409 Td [(\030)]TJ/F121 7.5716 Tf 5.339 5.945 Td [(#)]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F121 7.5716 Tf -7.171 -8.624 Td [(1)]TJ/F121 9.9626 Tf 14.222 2.679 Td [(\024)]TJ/F123 9.9626 Tf 10.548 0 Td [(x)]TJ/F151 9.9626 Tf 5.31 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.11 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 9.9626 Tf 7.051 -4.115 Td [(D)]TJ/F123 9.9626 Tf 10.787 0 Td [(W)]TJ/F121 7.5716 Tf 9.574 4.115 Td [(")]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F123 9.9626 Tf 4.403 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ -8.266 -8.435 Td [(1)]TJ/F126 9.9626 Tf 12.55 3.33 Td [(/;)]TJ/F117 9.9626 Tf 48.026 0 Td [(\0503.12\051)]TJ ET 1 0 0 1 39.797 426.409 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -426.409 cm BT /F117 9.9626 Tf 39.797 403.993 Td [(where)]TJ/F123 9.9626 Tf 27.078 0 Td [(W)]TJ/F121 7.5716 Tf 9.574 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 6.775 -3.616 Td [(is)-250(the)-250(scale)-250(function)-250(of)-250(the)-250(spectrally)-250(ne)15(g)5(ati)25(v)15(e)-250(L)]TJ 190.867 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-250(process)]TJ/F126 9.9626 Tf 49.245 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.616 Td [(.)]TJ ET 1 0 0 1 39.797 403.993 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -403.993 cm BT /F117 9.9626 Tf 51.752 392.212 Td [(This)-355(observ)25(ation)-355(re\003ects)-355(the)-355(duality)-356(property)-355(for)-355(positi)25(v)15(e)-355(self-similar)-355(Mark)10(o)15(v)-355(processes)-355(in)]TJ ET 1 0 0 1 39.797 392.212 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -392.212 cm BT /F117 9.9626 Tf 39.797 380.257 Td [(this)-306(particular)-306(case)-306(\050see)-306(Section)]TJ ET 1 0 0 1 170.684 380.257 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -170.684 -380.257 cm BT /F117 9.9626 Tf 170.684 380.257 Td [(2)]TJ ET 1 0 0 1 175.665 380.257 cm 0 g 0 G 1 0 0 1 -175.665 -380.257 cm BT /F117 9.9626 Tf 178.714 380.257 Td [(in)-306(Bertoin)-306(and)-306(Y)110(or)-306([)]TJ ET 1 0 0 1 260.646 380.257 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -260.646 -380.257 cm BT /F117 9.9626 Tf 260.646 380.257 Td [(4)]TJ ET 1 0 0 1 265.627 380.257 cm 0 g 0 G 1 0 0 1 -265.627 -380.257 cm BT /F117 9.9626 Tf 265.627 380.257 Td [(]\051.)-306(More)-306(precisely)65(,)-306(we)-306(ha)20(v)15(e)-306(the)-306(duality)]TJ ET 1 0 0 1 39.797 380.257 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -380.257 cm BT /F117 9.9626 Tf 39.797 366.948 Td [(property)-361(between)-361(the)-361(resolv)15(ent)-360(operators)-361(of)]TJ/F126 9.9626 Tf 182.436 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(")]TJ/F123 7.5716 Tf 0.205 -6.716 Td [(x)]TJ/F126 9.9626 Tf 4.957 1.611 Td [(/)]TJ/F117 9.9626 Tf 3.717 0 Td [(,)-361(with)-361(underlying)-361(L)]TJ 80.798 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-361(process)]TJ/F126 9.9626 Tf 51.454 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.617 Td [(,)-361(and)]TJ ET 1 0 0 1 39.797 366.948 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -366.948 cm BT /F126 9.9626 Tf 39.797 353.64 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(#)]TJ/F123 7.5716 Tf 0.204 -6.717 Td [(x)]TJ/F126 9.9626 Tf 4.958 1.612 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)-250(for)]TJ/F123 9.9626 Tf 19.358 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0,)-250(with)-250(underlying)-250(L)]TJ 82.465 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-250(process)]TJ/F126 9.9626 Tf 49.245 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(p)]TJ/F117 9.9626 Tf 4.283 -3.617 Td [(.)]TJ ET 1 0 0 1 39.797 353.64 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -353.64 cm BT /F117 9.9626 Tf 51.752 341.859 Td [(From)-312(the)-311(identi\002cation)-312(of)-312(the)-311(scale)-312(function)-312(in)]TJ ET 1 0 0 1 244.281 341.859 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -244.281 -341.859 cm BT /F117 9.9626 Tf 244.281 341.859 Td [(\0503.12\051)]TJ ET 1 0 0 1 268.351 341.859 cm 0 g 0 G 1 0 0 1 -268.351 -341.859 cm BT /F117 9.9626 Tf 271.456 341.859 Td [(and)]TJ ET 1 0 0 1 288.947 341.859 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -288.947 -341.859 cm BT /F117 9.9626 Tf 288.947 341.859 Td [(Lemma)-312(2)]TJ ET 1 0 0 1 327.469 341.859 cm 0 g 0 G 1 0 0 1 -327.469 -341.859 cm BT /F117 9.9626 Tf 327.469 341.859 Td [(,)-312(it)-311(is)-312(possible)-312(to)-311(gi)25(v)15(e)-312(a)]TJ ET 1 0 0 1 39.797 341.859 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -341.859 cm BT /F117 9.9626 Tf 39.797 329.904 Td [(triple)-250(la)15(w)-250(for)-250(the)-250(process)]TJ/F126 9.9626 Tf 101.388 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F117 9.9626 Tf 6.774 -3.616 Td [(at)-250(\002rst)-250(passage)-250(o)15(v)15(er)-250(the)-250(le)25(v)15(el)]TJ/F123 9.9626 Tf 117.439 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0.)]TJ ET 1 0 0 1 39.797 329.904 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -20.69 cm 0 g 0 G 1 0 0 1 -35.812 -309.214 cm BT /F124 9.9626 Tf 39.797 309.214 Td [(Lemma)-250(3.)]TJ ET 1 0 0 1 82.407 309.214 cm 0 g 0 G 1 0 0 1 -82.407 -309.214 cm BT /F123 9.9626 Tf 86.392 309.214 Td [(Let)]TJ ET q 1 0 0 1 101.794 317.393 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 101.794 309.214 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F123 7.5716 Tf -7.17 -8.624 Td [(t)]TJ/F121 9.9626 Tf 14.221 2.68 Td [(D)]TJ/F117 9.9626 Tf 10.539 0 Td [(sup)]TJ/F117 7.5716 Tf 13.838 -2.536 Td [(0)]TJ/F121 7.5716 Tf 3.785 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(t)]TJ/F126 9.9626 Tf 4.945 2.536 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.305 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F123 7.5716 Tf -8.266 -6.917 Td [(s)]TJ/F123 9.9626 Tf 12.55 1.612 Td [(.)-250(F)105(or)-300(x)]TJ/F126 9.9626 Tf 29.945 0 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0)]TJ/F123 9.9626 Tf 4.981 0 Td [(,)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.28 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)-167(\036)]TJ/F121 9.9626 Tf 13.972 0 Td [(\025)]TJ/F126 9.9626 Tf 10.279 0 Td [(\021)]TJ/F123 9.9626 Tf 7.87 0 Td [(and)]TJ/F126 9.9626 Tf 17.704 0 Td [(\021)]TJ/F121 9.9626 Tf 8.147 0 Td [(2)-278(T)]TJ/F117 9.9626 Tf 12.351 0 Td [(0)]TJ/F126 9.9626 Tf 4.982 0 Td [(;)]TJ/F123 9.9626 Tf 5.227 0 Td [(x)]TJ/F121 9.9626 Tf 5.31 0 Td [(U)]TJ/F123 9.9626 Tf 5.808 0 Td [(we)-250(have)]TJ ET 1 0 0 1 39.797 309.214 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -309.214 cm BT /F123 9.9626 Tf 64.584 287.929 Td [(P)]TJ/F151 9.9626 Tf 8.564 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -10.999 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.305 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F123 7.5716 Tf -8.092 -10.233 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.277 -4.609 Td [(x)]TJ/F121 9.9626 Tf 10.514 6.255 Td [(\000)]TJ/F123 9.9626 Tf 10.254 0 Td [(x)]TJ/F121 9.9626 Tf 8.077 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)-87(;)]TJ/F123 9.9626 Tf 10.478 0 Td [(x)]TJ/F121 9.9626 Tf 7.524 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.305 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(p)]TJ/F123 7.5716 Tf -8.092 -10.233 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(C)]TJ/F123 5.9776 Tf -1.278 -4.609 Td [(x)]TJ/F121 7.5716 Tf 6.438 1.327 Td [(\000)]TJ/F121 9.9626 Tf 9.172 4.928 Td [(2)]TJ/F117 9.9626 Tf 9.033 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\036)-77(;)]TJ/F123 9.9626 Tf 11.742 0 Td [(x)]TJ/F121 9.9626 Tf 7.524 0 Td [(\000)]TJ ET q 1 0 0 1 225.288 296.108 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F126 9.9626 Tf 225.288 287.929 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.944 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(p)]TJ/F123 7.5716 Tf -6.996 -10.234 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.283 Td [(C)]TJ/F123 5.9776 Tf -1.277 -4.609 Td [(x)]TJ/F121 7.5716 Tf 6.438 1.326 Td [(\000)]TJ/F121 9.9626 Tf 9.171 4.29 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)]TJ/F151 9.9626 Tf 5.38 10.999 Td [(\021)]TJ ET 1 0 0 1 39.797 287.929 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -287.929 cm BT /F121 9.9626 Tf 73.67 268.19 Td [(D)]TJ/F123 9.9626 Tf 11.146 0 Td [(K)]TJ/F121 7.5716 Tf 8.01 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 5.944 -4.114 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 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7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F117 9.9626 Tf 5.124 -4.114 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ/F117 9.9626 Tf 5.38 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)]TJ/F117 9.9626 Tf 6.246 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\021)-20(;)]TJ ET 1 0 0 1 39.797 268.19 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -268.19 cm BT /F123 9.9626 Tf 39.797 250.953 Td [(wher)37(e)]TJ ET 1 0 0 1 39.797 250.953 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -250.953 cm BT /F123 9.9626 Tf 64.315 227.632 Td [(K)]TJ/F121 9.9626 Tf 10.777 0 Td [(D)]TJ/F117 9.9626 Tf 15.688 6.984 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.616 Td [(.\013)]TJ/F121 7.5716 Tf 7.451 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(2)]TJ/F126 7.5716 Tf 3.785 0 Td [(/v)]TJ ET q 1 0 0 1 86.826 230.123 cm []0 d 0 J 0.458 w 0 0 m 36.786 0 l S Q BT /F126 9.9626 Tf 86.826 220.559 Td [(\013)-40(.\013)]TJ/F121 9.9626 Tf 18.104 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F151 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[(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 3.616 Td [(v)]TJ/F126 9.9626 Tf 4.489 -3.616 Td [(/)]TJ/F126 7.5716 Tf 3.716 3.616 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET q 1 0 0 1 227.054 230.123 cm []0 d 0 J 0.458 w 0 0 m 48.34 0 l S Q BT /F126 9.9626 Tf 232.831 220.559 Td [(\013)-40(.\013)]TJ/F121 9.9626 Tf 18.104 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ 33.737 14.057 Td [(\031)]TJ ET q 1 0 0 1 277.785 230.123 cm []0 d 0 J 0.458 w 0 0 m 50.681 0 l S Q BT /F117 9.9626 Tf 277.785 220.559 Td [(sin)]TJ/F126 9.9626 Tf 13.286 0 Td [(\031)-72(.\013)]TJ/F121 9.9626 Tf 18.712 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ 4.912 7.073 Td [(:)]TJ ET 1 0 0 1 39.797 227.632 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -227.632 cm BT /F117 9.9626 Tf 51.752 197.619 Td 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Tf 45.354 607.707 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 71.307 607.707 cm 0 g 0 G 1 0 0 1 -71.307 -607.707 cm BT /F117 9.9626 Tf 75.292 607.707 Td [(Recall)-250(that)-250(the)-250(Laplace)-250(e)15(xponent)-250(of)]TJ/F126 9.9626 Tf 143.72 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 6.775 -3.616 Td [(is)-250(gi)25(v)15(en)-250(by)]TJ ET 1 0 0 1 45.354 607.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -607.707 cm BT /F126 9.9626 Tf 69.265 583.699 Td [(\040)]TJ/F121 7.5716 Tf 7.91 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.\022)-100(/)]TJ/F121 9.9626 Tf 15.58 0 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(m)]TJ/F40 9.9626 Tf 10.38 6.983 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(C)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)-40(/)]TJ ET q 1 0 0 1 117.431 586.189 cm []0 d 0 J 0.458 w 0 0 m 41.48 0 l S Q BT /F40 9.9626 Tf 117.431 576.625 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)-100(/)]TJ/F40 9.9626 Tf 12.812 0 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.\013)-40(/)]TJ/F117 9.9626 Tf 24.677 7.074 Td [(for)]TJ/F126 9.9626 Tf 14.107 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.982 0 Td [(:)]TJ ET 1 0 0 1 45.354 583.699 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -583.699 cm BT /F117 9.9626 Tf 45.354 558.202 Td [(Hence)-411(from)]TJ ET 1 0 0 1 98.347 558.202 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -98.347 -558.202 cm BT /F117 9.9626 Tf 98.347 558.202 Td [(Proposition)-411(1)]TJ ET 1 0 0 1 153.367 558.202 cm 0 g 0 G 1 0 0 1 -153.367 -558.202 cm BT /F117 9.9626 Tf 153.367 558.202 Td [(,)-411(we)-410(get)-411(that)-411(the)-410(Laplace)-411(transform)-410(of)]TJ/F126 9.9626 Tf 164.69 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.616 Td [(,)-411(here)-410(denoted)-411(by)]TJ/F126 9.9626 Tf 77.504 0 Td [(\040)]TJ/F121 7.5716 Tf 7.911 3.616 Td [(#)]TJ/F117 9.9626 Tf 5.162 -3.616 Td [(,)]TJ ET 1 0 0 1 45.354 558.202 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -558.202 cm BT /F117 9.9626 Tf 45.354 546.247 Td [(satis\002es)]TJ ET 1 0 0 1 45.354 546.247 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -546.247 cm BT /F126 9.9626 Tf 69.265 524.281 Td [(\040)]TJ/F121 7.5716 Tf 7.91 4.114 Td [(#)]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.\022)-100(/)]TJ/F121 9.9626 Tf 15.58 0 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(\040)]TJ/F121 7.5716 Tf 7.91 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 10.539 0 Td [(m)]TJ/F40 9.9626 Tf 10.38 6.984 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)-40(/)]TJ ET q 1 0 0 1 173.801 526.771 cm []0 d 0 J 0.458 w 0 0 m 58.66 0 l S Q BT /F40 9.9626 Tf 173.801 517.207 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F40 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(/)]TJ/F117 9.9626 Tf 24.678 7.074 Td [(for)]TJ/F126 9.9626 Tf 14.107 0 Td [(\022)]TJ/F121 9.9626 Tf 8.147 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(1)]TJ ET 1 0 0 1 45.354 524.281 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -524.281 cm BT /F117 9.9626 Tf 45.354 500.606 Td [(which)-286(is)-287(also)-286(v)25(alid)-286(for)]TJ/F126 9.9626 Tf 92.6 0 Td [(\022)]TJ/F121 9.9626 Tf 8.818 0 Td [(\025)]TJ/F117 9.9626 Tf 10.95 0 Td [(0,)-286(since)-287(an)15(y)-286(spectrally)-286(ne)15(g)5(ati)25(v)15(e)-287(L)]TJ 134.977 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-286(process)-287(has)-286(\002nite)-286(e)15(xponential)]TJ ET 1 0 0 1 45.354 500.606 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -500.606 cm BT /F117 9.9626 Tf 45.354 488.651 Td [(moments)-250(\050see)-250(for)-250(instance)-250([)]TJ ET 1 0 0 1 155.47 488.651 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -155.47 -488.651 cm BT /F117 9.9626 Tf 155.47 488.651 Td [(2)]TJ ET 1 0 0 1 160.451 488.651 cm 0 g 0 G 1 0 0 1 -160.451 -488.651 cm BT /F117 9.9626 Tf 160.451 488.651 Td [(,)]TJ ET 1 0 0 1 162.942 488.651 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -162.942 -488.651 cm BT /F117 9.9626 Tf 162.942 488.651 Td [(28)]TJ ET 1 0 0 1 172.905 488.651 cm 0 g 0 G 1 0 0 1 -172.905 -488.651 cm BT /F117 9.9626 Tf 172.905 488.651 Td [(]\051.)]TJ ET 1 0 0 1 45.354 488.651 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -488.651 cm BT /F117 9.9626 Tf 57.31 476.171 Td [(No)25(w)65(,)-248(recall)-248(that)-248(the)-249(Laplace)-248(transform)-248(of)-248(the)-248(scale)-248(function)-248(of)]TJ/F126 9.9626 Tf 249.559 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(#)]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.617 Td [(,)-248(here)-248(denoted)-248(by)]TJ/F123 9.9626 Tf 71.279 0 Td [(W)]TJ/F121 7.5716 Tf 9.574 3.617 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F123 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.625 -3.617 Td [(,)-248(is)]TJ ET 1 0 0 1 45.354 476.171 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -476.171 cm BT /F117 9.9626 Tf 45.354 464.216 Td [(gi)25(v)15(en)-250(by)-250(the)-250(in)40(v)15(erse)-250(of)]TJ/F126 9.9626 Tf 92.852 0 Td [(\040)]TJ/F121 7.5716 Tf 7.91 3.617 Td [(#)]TJ/F117 9.9626 Tf 5.162 -3.617 Td [(.)-250(Since,)-250(for)]TJ/F126 9.9626 Tf 46.207 0 Td [(\022)-378(>)]TJ/F117 9.9626 Tf 18.685 0 Td [(1,)-250(we)-250(ha)20(v)15(e)-250(that)]TJ ET 1 0 0 1 45.354 464.216 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -464.216 cm BT /F40 9.9626 Tf 70.46 445.22 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F40 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.\013)-40(/)]TJ ET q 1 0 0 1 70.46 440.727 cm []0 d 0 J 0.458 w 0 0 m 58.66 0 l S Q BT /F40 9.9626 Tf 71.864 431.163 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\022)]TJ/F121 9.9626 Tf 11.31 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)-40(/)]TJ/F121 9.9626 Tf 15.17 7.073 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.559 Td [(Z)]TJ/F117 7.5716 Tf 9.823 -2.922 Td [(1)]TJ -4.563 -19.593 Td [(0)]TJ/F123 9.9626 Tf 10.507 8.956 Td [(u)]TJ/F126 7.5716 Tf 5.51 4.115 Td [(.\022)]TJ/F121 7.5716 Tf 6.913 0 Td [(\000)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F121 7.5716 Tf 2.824 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F123 9.9626 Tf 9.985 0 Td [(u)]TJ/F126 9.9626 Tf 5.51 0 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F123 9.9626 Tf 4.981 0 Td [(u)]TJ/F121 9.9626 Tf 8.277 0 Td [(D)]TJ/F151 9.9626 Tf 10.538 13.559 Td [(Z)]TJ/F121 7.5716 Tf 9.823 -2.922 Td [(1)]TJ/F117 7.5716 Tf -4.563 -19.593 Td [(0)]TJ/F117 9.9626 Tf 14.452 8.956 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F123 7.5716 Tf 4.293 0 Td [(x)]TJ/F117 9.9626 Tf 4.534 -4.115 Td [(e)]TJ/F123 7.5716 Tf 4.628 4.115 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.11 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(d)]TJ/F123 9.9626 Tf 5.25 0 Td [(x)]TJ/F126 9.9626 Tf 5.311 0 Td [(;)]TJ ET 1 0 0 1 45.354 438.236 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -438.236 cm BT /F117 9.9626 Tf 45.354 414.356 Td [(and)-250(hence)]TJ ET 1 0 0 1 45.354 414.356 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -414.356 cm BT /F123 9.9626 Tf 69.514 392.44 Td [(W)]TJ/F121 7.5716 Tf 9.574 4.115 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)]TJ/F117 9.9626 Tf 13.133 6.984 Td [(1)]TJ ET q 1 0 0 1 118.054 394.931 cm []0 d 0 J 0.458 w 0 0 m 7.781 0 l S Q BT /F123 9.9626 Tf 118.054 385.367 Td [(m)]TJ/F126 9.9626 Tf 8.977 7.073 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F123 7.5716 Tf 6.11 0 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 4.284 -4.115 Td [(e)]TJ/F123 7.5716 Tf 4.628 4.115 Td [(x)]TJ/F126 9.9626 Tf 4.534 -4.115 Td [(;)]TJ ET 1 0 0 1 45.354 392.44 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -392.44 cm BT /F117 9.9626 Tf 45.354 370.4 Td [(as)-250(required.)]TJ/F116 9.9626 Tf 58.929 0 Td [(\004)]TJ ET 1 0 0 1 45.354 370.4 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -370.4 cm BT /F117 9.9626 Tf 57.31 350.369 Td [(One)-302(may)-301(also)-302(write)-302(do)25(wn)-301(a)-302(triple)-302(la)15(w)-301(for)-302(the)-302(\002rst)-302(passage)-301(problem)-302(of)]TJ/F126 9.9626 Tf 285.713 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F117 9.9626 Tf 7.289 -3.616 Td [(as)-302(we)-301(ha)20(v)15(e)-302(seen)]TJ ET 1 0 0 1 45.354 350.369 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -350.369 cm BT /F117 9.9626 Tf 45.354 338.413 Td [(before)-250(for)]TJ/F126 9.9626 Tf 42.042 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.617 Td [(.)]TJ ET 1 0 0 1 45.354 338.413 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.857 cm 0 g 0 G 1 0 0 1 -41.369 -315.556 cm BT /F124 9.9626 Tf 45.354 315.556 Td [(Lemma)-250(5.)]TJ ET 1 0 0 1 87.964 315.556 cm 0 g 0 G 1 0 0 1 -87.964 -315.556 cm BT /F123 9.9626 Tf 91.949 315.556 Td [(F)105(or)]TJ/F126 9.9626 Tf 16.618 0 Td [(v)-318(<)]TJ/F117 9.9626 Tf 18.556 0 Td [(0)]TJ/F123 9.9626 Tf 4.981 0 Td [(,)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F121 9.9626 Tf 8.148 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)-167(\036)]TJ/F121 9.9626 Tf 13.972 0 Td [(\025)]TJ/F126 9.9626 Tf 10.279 0 Td [(\021)]TJ/F123 9.9626 Tf 7.871 0 Td [(and)]TJ/F126 9.9626 Tf 17.703 0 Td [(\021)]TJ/F121 9.9626 Tf 8.147 0 Td [(2)-278(T)]TJ/F117 9.9626 Tf 12.352 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F121 9.9626 Tf 4.958 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(v)]TJ/F121 9.9626 Tf 5.25 0 Td [(U)]TJ/F123 9.9626 Tf 5.808 0 Td [(we)-250(have)]TJ ET 1 0 0 1 45.354 315.556 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -315.556 cm BT /F123 9.9626 Tf 70.141 294.133 Td [(P)]TJ/F151 9.9626 Tf 8.565 10.999 Td [(\020)]TJ/F126 9.9626 Tf 5.429 -10.999 Td [(v)]TJ/F121 9.9626 Tf 7.465 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 5.105 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F123 7.5716 Tf -8.092 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 9.9626 Tf 11.229 6.165 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)-87(;)-167(\030)]TJ/F121 7.5716 Tf 15.548 5.105 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F123 7.5716 Tf -8.092 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.439 -4.519 Td [(v)]TJ/F121 7.5716 Tf 6.599 1.237 Td [(\000)]TJ/F121 9.9626 Tf 8.618 4.928 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(v)]TJ/F121 9.9626 Tf 8.018 0 Td [(2)]TJ/F117 9.9626 Tf 9.033 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\036)-77(;)-167(\030)]TJ ET q 1 0 0 1 212.41 290.646 cm []0 d 0 J 0.458 w 0 0 m 5.34 0 l S Q BT /F121 7.5716 Tf 217.75 299.238 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F123 7.5716 Tf -6.997 -10.033 Td [(T)]TJ/F121 5.9776 Tf 5.353 3.282 Td [(\000)]TJ/F126 5.9776 Tf -1.438 -4.519 Td [(v)]TJ/F121 7.5716 Tf 6.599 1.237 Td [(\000)]TJ/F121 9.9626 Tf 8.618 4.928 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(v)]TJ/F121 9.9626 Tf 8.017 0 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)]TJ/F151 9.9626 Tf 5.38 10.999 Td [(\021)]TJ ET 1 0 0 1 45.354 294.133 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -294.133 cm BT /F121 9.9626 Tf 79.227 274.356 Td [(D)]TJ/F123 9.9626 Tf 11.146 0 Td [(K)]TJ/F121 7.5716 Tf 8.01 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F117 9.9626 Tf 5.944 -4.115 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F123 7.5716 Tf 5.868 0 Td [(q)]TJ/F126 7.5716 Tf 4.353 0 Td [(.\036)]TJ/F121 7.5716 Tf 7.572 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\021)-20(/)]TJ/F126 9.9626 Tf 7.411 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(.v)]TJ/F121 7.5716 Tf 6.814 0 Td [(C)]TJ/F126 7.5716 Tf 5.906 0 Td [(\021)-20(/)]TJ/F121 9.9626 Tf 9.625 -4.115 Td [(C)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)]TJ/F121 9.9626 Tf 8.301 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(2)]TJ/F126 9.9626 Tf 4.981 0 Td [(/.)]TJ/F117 9.9626 Tf 7.432 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F121 7.5716 Tf 3.991 0 Td [(C)]TJ/F126 7.5716 Tf 5.905 0 Td [(\021)]TJ/F126 9.9626 Tf 4.587 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(2)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\022)]TJ/F121 7.5716 Tf 4.089 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\036)]TJ/F126 9.9626 Tf 5.245 -4.115 Td [(/)]TJ/F126 7.5716 Tf 3.716 4.115 Td [(\013)]TJ/F126 9.9626 Tf 5.125 -4.115 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(e)]TJ/F121 7.5716 Tf 4.423 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\022)]TJ/F121 7.5716 Tf 4.089 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\036)]TJ/F126 9.9626 Tf 5.245 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F117 9.9626 Tf 5.124 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\022)]TJ/F117 9.9626 Tf 5.38 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)]TJ/F117 9.9626 Tf 6.247 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)-20(;)]TJ ET 1 0 0 1 45.354 274.356 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -274.356 cm BT /F123 9.9626 Tf 45.354 255.374 Td 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0 Td [(\013)]TJ/F117 9.9626 Tf 5.124 -4.115 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)]TJ/F117 9.9626 Tf 6.247 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)-20(:)]TJ ET 1 0 0 1 45.354 230.295 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -35.146 cm 0 g 0 G 1 0 0 1 -41.369 -195.149 cm BT /F124 9.9626 Tf 45.354 195.149 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 71.307 195.149 cm 0 g 0 G 1 0 0 1 -71.307 -195.149 cm BT /F117 9.9626 Tf 75.292 195.149 Td [(First)-257(recall)-256(that)-257(the)-257(process)]TJ/F126 9.9626 Tf 110.18 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(#)]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 6.841 -3.617 Td [(drifts)-257(to)25(w)10(ards)]TJ/F121 9.9626 Tf 57.338 0 Td [(\0001)]TJ/F117 9.9626 Tf 20.501 0 Td [(a.s.)-257(Ag)5(ain,)-256(we)-257(ha)20(v)15(e)-257(from)-257(Exam)1(p)-1(l)1(e)-257(8)]TJ ET 1 0 0 1 45.354 195.149 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -195.149 cm BT /F117 9.9626 Tf 45.354 183.194 Td 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9.984 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\021)-20(/\031)]TJ/F121 7.5716 Tf 16.069 4.115 Td [(#)]TJ/F126 9.9626 Tf 5.163 -4.115 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.77 0 Td [(\022)]TJ/F121 9.9626 Tf 7.594 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\036)-50(/)]TJ/F117 9.9626 Tf 9.962 0 Td [(d)]TJ/F126 9.9626 Tf 4.982 0 Td [(\022)]TJ/F117 9.9626 Tf 5.38 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)-77(;)]TJ ET 1 0 0 1 45.354 164.212 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -164.212 cm BT /F117 9.9626 Tf 45.354 145.23 Td [(where)]TJ/F123 9.9626 Tf 26.796 0 Td [(q)]TJ/F126 9.9626 Tf 8.526 0 Td [(>)]TJ/F117 9.9626 Tf 10.569 0 Td [(0)-252(is)-251(the)-252(killing)-252(rate)-251(of)-252(the)-251(descending)-252(ladder)-252(height)-251(process)-252(\050see)-252(for)-251(instance)-252(Chapter)]TJ ET 1 0 0 1 45.354 145.23 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -145.23 cm BT /F117 9.9626 Tf 45.354 133.275 Td [(VI)-250(in)-250(Bertoin)-250([)]TJ ET 1 0 0 1 104.293 133.275 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -104.293 -133.275 cm BT /F117 9.9626 Tf 104.293 133.275 Td [(2)]TJ ET 1 0 0 1 109.274 133.275 cm 0 g 0 G 1 0 0 1 -109.274 -133.275 cm BT /F117 9.9626 Tf 109.274 133.275 Td [(])-250(for)-250(a)-250(proper)-250(de\002nition\051)-250(of)]TJ/F126 9.9626 Tf 110.116 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(#)]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F117 9.9626 Tf 4.284 -3.616 Td [(.)]TJ ET 1 0 0 1 45.354 133.275 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -133.275 cm BT /F117 9.9626 Tf 57.31 120.795 Td [(Hence)-250(the)-250(triple)-250(la)15(w)-250(of)-250(interest)-250(has)-250(a)-250(density)-250(with)-250(respect)-250(to)-250(d)]TJ/F126 9.9626 Tf 245.546 0 Td [(\022)]TJ/F117 9.9626 Tf 5.38 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\036)]TJ/F117 9.9626 Tf 6.247 0 Td [(d)]TJ/F126 9.9626 Tf 4.981 0 Td [(\021)]TJ/F117 9.9626 Tf 7.87 0 Td [(which)-250(is)-250(proportional)-250(to)]TJ ET 1 0 0 1 45.354 120.795 cm 0 g 0 G 0 g 0 G 1 0 0 1 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9.9626 Tf 10.622 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(/)]TJ ET q 1 0 0 1 154.081 315.532 cm []0 d 0 J 0.458 w 0 0 m 61.279 0 l S Q BT /F123 9.9626 Tf 179.834 305.885 Td [(a)]TJ/F117 7.5716 Tf 5.459 2.88 Td [(2)]TJ/F126 9.9626 Tf 31.262 4.277 Td [(:)]TJ ET 1 0 0 1 39.797 313.042 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -313.042 cm BT /F117 9.9626 Tf 39.797 288.767 Td [(It)-250(no)25(w)-250(follo)25(ws)-250(taking)-250(limits)-250(as)]TJ/F123 9.9626 Tf 123.455 0 Td [(a)]TJ/F121 9.9626 Tf 8.227 0 Td [(")-278(1)]TJ/F117 9.9626 Tf 21.567 0 Td [(that)]TJ ET 1 0 0 1 39.797 288.767 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -288.767 cm BT /F123 9.9626 Tf 63.707 260.837 Td [(u)]TJ/F126 9.9626 Tf 5.51 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 5.595 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F117 9.9626 Tf 29.575 6.984 Td [(1)]TJ ET q 1 0 0 1 107.266 263.328 cm []0 d 0 J 0.458 w 0 0 m 40.664 0 l S Q BT /F117 9.9626 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[(2)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET q 1 0 0 1 246.877 263.328 cm []0 d 0 J 0.458 w 0 0 m 41.75 0 l S Q BT /F126 9.9626 Tf 246.877 253.681 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(u)]TJ/F121 9.9626 Tf 7.723 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F117 7.5716 Tf 3.716 2.879 Td [(1)]TJ/F126 7.5716 Tf 3.785 0 Td [(=)]TJ/F117 7.5716 Tf 3.559 0 Td [(2)]TJ/F117 9.9626 Tf 5.479 4.277 Td [(d)]TJ/F123 9.9626 Tf 4.982 0 Td [(u)]TJ/F126 9.9626 Tf 5.509 0 Td [(:)]TJ ET 1 0 0 1 39.797 260.837 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -260.837 cm BT /F117 9.9626 Tf 39.797 236.646 Td [(According)-250(to)-250(the)-250(method)-250(presented)-250(in)-250(Getoor)-250([)]TJ ET 1 0 0 1 226.007 236.646 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -226.007 -236.646 cm BT /F117 9.9626 Tf 226.007 236.646 Td [(17)]TJ ET 1 0 0 1 235.97 236.646 cm 0 g 0 G 1 0 0 1 -235.97 -236.646 cm BT /F117 9.9626 Tf 235.97 236.646 Td [(])-250(one)-250(may)-250(compute)]TJ ET 1 0 0 1 39.797 236.646 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -236.646 cm BT /F124 9.9626 Tf 63.707 217.375 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.494 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 7.5716 Tf 6.804 -1.494 Td [(\033)]TJ/F121 5.9776 Tf 4.043 -1.219 Td [(f)]TJ/F123 5.9776 Tf 2.194 0 Td [(a)]TJ/F126 5.9776 Tf 3.276 0 Td [(;)]TJ/F123 5.9776 Tf 1.978 0 Td [(b)]TJ/F121 5.9776 Tf 3.109 0 Td [(g)]TJ/F121 9.9626 Tf 5.975 2.713 Td [(D)]TJ/F123 9.9626 Tf 10.508 0 Td [(a)]TJ/F121 9.9626 Tf 5.46 0 Td [(I)]TJ/F126 9.9626 Tf 6.877 0 Td [(\033)]TJ/F121 7.5716 Tf 5.32 -1.494 Td [(f)]TJ/F123 7.5716 Tf 2.779 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(;)]TJ/F123 7.5716 Tf 2.507 0 Td [(b)]TJ/F121 7.5716 Tf 3.937 0 Td [(g)]TJ/F126 9.9626 Tf 6.067 1.494 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.295 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.625 Td [(0)]TJ/F126 9.9626 Tf 7.699 3.33 Td [(/)]TJ ET 1 0 0 1 39.797 217.375 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -217.375 cm BT /F117 9.9626 Tf 39.797 198.105 Td [(where)]TJ/F126 9.9626 Tf 27.925 0 Td [(\033)]TJ/F121 7.5716 Tf 5.32 -1.494 Td [(f)]TJ/F123 7.5716 Tf 2.779 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(;)]TJ/F123 7.5716 Tf 2.506 0 Td [(b)]TJ/F121 7.5716 Tf 3.937 0 Td [(g)]TJ/F121 9.9626 Tf 8.097 1.494 Td [(D)]TJ/F117 9.9626 Tf 12.568 0 Td [(inf)]TJ/F121 9.9626 Tf 11.068 0 Td [(f)]TJ/F123 9.9626 Tf 3.686 0 Td [(t)]TJ/F126 9.9626 Tf 8.463 0 Td [(>)]TJ/F117 9.9626 Tf 12.568 0 Td [(0)]TJ/F121 9.9626 Tf 9.778 0 Td [(V)]TJ/F123 9.9626 Tf 8.304 0 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.494 Td [(t)]TJ/F121 9.9626 Tf 8.081 1.494 Td [(D)]TJ/F123 9.9626 Tf 12.538 0 Td [(a)]TJ/F117 9.9626 Tf 7.95 0 Td [(or)]TJ/F123 9.9626 Tf 10.79 0 Td [(b)]TJ/F121 9.9626 Tf 5.18 0 Td [(g)]TJ/F117 9.9626 Tf 7.273 0 Td [(and)]TJ/F123 9.9626 Tf 17.943 0 Td [(a)]TJ/F126 9.9626 Tf 5.459 0 Td [(;)]TJ/F123 9.9626 Tf 4.958 0 Td [(b)]TJ/F126 9.9626 Tf 9.978 0 Td [(>)]TJ/F117 9.9626 Tf 12.567 0 Td [(0)-360(using)-360(the)-360(follo)25(wing)-360(technique.)-361(The)]TJ ET 1 0 0 1 39.797 198.105 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -198.105 cm BT /F117 9.9626 Tf 39.797 186.15 Td [(tw)10(o-point)-250(hitting)-250(probability)-250(in)-250(Getoor)-250([)]TJ ET 1 0 0 1 199.377 186.15 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -199.377 -186.15 cm BT /F117 9.9626 Tf 199.377 186.15 Td [(17)]TJ ET 1 0 0 1 209.339 186.15 cm 0 g 0 G 1 0 0 1 -209.339 -186.15 cm BT /F117 9.9626 Tf 209.339 186.15 Td [(])-250(is)-250(gi)25(v)15(en)-250(by)-250(the)-250(formula)]TJ ET 1 0 0 1 39.797 186.15 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -186.15 cm BT /F124 9.9626 Tf 63.707 161.854 Td [(P)]TJ/F123 7.5716 Tf 6.292 -1.495 Td [(x)]TJ/F126 9.9626 Tf 4.534 1.495 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 7.5716 Tf 6.804 -1.495 Td [(\033)]TJ/F121 5.9776 Tf 4.043 -1.218 Td [(f)]TJ/F123 5.9776 Tf 2.194 0 Td [(a)]TJ/F126 5.9776 Tf 3.276 0 Td [(;)]TJ/F123 5.9776 Tf 1.978 0 Td [(b)]TJ/F121 5.9776 Tf 3.109 0 Td [(g)]TJ/F121 9.9626 Tf 5.975 2.713 Td [(D)]TJ/F123 9.9626 Tf 10.508 0 Td [(a)]TJ/F121 9.9626 Tf 5.46 0 Td [(I)]TJ/F126 9.9626 Tf 6.877 0 Td [(\033)]TJ/F121 7.5716 Tf 5.32 -1.495 Td [(f)]TJ/F123 7.5716 Tf 2.779 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(;)]TJ/F123 7.5716 Tf 2.507 0 Td [(b)]TJ/F121 7.5716 Tf 3.937 0 Td [(g)]TJ/F126 9.9626 Tf 6.067 1.495 Td [(<)-278(\033)]TJ/F121 7.5716 Tf 17.153 4.294 Td [(\000)]TJ/F117 7.5716 Tf -1.295 -7.625 Td [(0)]TJ/F126 9.9626 Tf 7.699 3.331 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 19.529 6.983 Td [(q)]TJ/F126 9.9626 Tf 5.729 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 4.928 0 Td [(a)]TJ/F126 9.9626 Tf 5.459 0 Td [(/)]TJ ET q 1 0 0 1 203.544 164.344 cm []0 d 0 J 0.458 w 0 0 m 29.227 0 l S Q BT /F123 9.9626 Tf 203.494 154.78 Td [(q)]TJ/F126 9.9626 Tf 5.729 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 5.227 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ ET 1 0 0 1 39.797 161.854 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -161.854 cm BT /F117 9.9626 Tf 39.797 137.662 Td [(where)-250(the)]TJ/F121 9.9626 Tf 41.494 0 Td [(f)]TJ/F123 9.9626 Tf 3.955 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 4.928 0 Td [(a)]TJ/F126 9.9626 Tf 5.46 0 Td [(;)]TJ/F123 9.9626 Tf 4.958 0 Td [(b)]TJ/F121 9.9626 Tf 5.18 0 Td [(g)-222(\002)-222(f)]TJ/F123 9.9626 Tf 19.88 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 4.928 0 Td [(a)]TJ/F126 9.9626 Tf 5.46 0 Td [(;)]TJ/F123 9.9626 Tf 4.958 0 Td [(b)]TJ/F121 9.9626 Tf 5.181 0 Td [(g)]TJ/F117 9.9626 Tf 3.686 0 Td [(-matrix)]TJ/F123 9.9626 Tf 32.527 0 Td [(Q)]TJ/F117 9.9626 Tf 10.232 0 Td [(is)-250(de\002ned)-250(by)]TJ ET 1 0 0 1 39.797 137.662 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -137.662 cm BT /F123 9.9626 Tf 64.415 118.392 Td [(Q)]TJ/F121 9.9626 Tf 10.508 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 18.149 0 Td [(U)]TJ/F121 7.5716 Tf 8.329 4.114 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 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0 Td [(1)]TJ/F123 9.9626 Tf 6.466 -4.115 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(e)]TJ/F126 7.5716 Tf 4.423 4.115 Td [(v)]TJ/F126 9.9626 Tf 4.489 -4.115 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(e)]TJ/F123 7.5716 Tf 4.423 4.115 Td [(u)]TJ/F126 9.9626 Tf 4.685 -4.115 Td [(/)]TJ ET 1 0 0 1 45.354 400.113 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -400.113 cm BT /F123 9.9626 Tf 45.354 379.047 Td [(wher)37(e)]TJ ET 1 0 0 1 45.354 379.047 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -379.047 cm BT /F123 9.9626 Tf 71.446 352.451 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 4.929 0 Td [(a)]TJ/F126 9.9626 Tf 5.459 0 Td [(;)]TJ/F123 9.9626 Tf 4.958 0 Td [(b)]TJ/F126 9.9626 Tf 5.181 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 7.5716 Tf 12.929 13.444 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 3.029 0 Td [(x)]TJ/F126 7.5716 Tf 4.036 0 Td [(;)]TJ/F123 7.5716 Tf 2.483 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(/)]TJ ET q 1 0 0 1 125.532 363.89 cm []0 d 0 J 0.458 w 0 0 m 20.708 0 l S Q BT /F123 7.5716 Tf 125.684 357.863 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(;)]TJ/F123 7.5716 Tf 2.484 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(/)]TJ/F121 9.9626 Tf 6.385 3.537 Td [(\000)]TJ/F123 7.5716 Tf 11.18 4.495 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 3.029 0 Td [(x)]TJ/F126 7.5716 Tf 4.036 0 Td [(;)]TJ/F123 7.5716 Tf 2.506 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(/)]TJ ET q 1 0 0 1 160.83 363.89 cm []0 d 0 J 0.458 w 0 0 m 20.519 0 l S Q BT /F123 7.5716 Tf 160.982 357.863 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(;)]TJ/F123 7.5716 Tf 2.506 0 Td [(b)]TJ/F126 7.5716 Tf 3.938 0 Td [(/)]TJ ET q 1 0 0 1 124.337 354.942 cm []0 d 0 J 0.458 w 0 0 m 58.208 0 l S Q BT /F123 7.5716 Tf 125.646 348.136 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.801 0 Td [(a)]TJ/F126 7.5716 Tf 4.15 0 Td [(;)]TJ/F123 7.5716 Tf 2.483 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(/)]TJ ET q 1 0 0 1 125.646 346.131 cm []0 d 0 J 0.458 w 0 0 m 20.595 0 l S Q BT /F123 7.5716 Tf 125.741 340.104 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(;)]TJ/F123 7.5716 Tf 2.484 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(/)]TJ/F121 9.9626 Tf 6.328 3.536 Td [(\000)]TJ/F123 7.5716 Tf 11.18 4.496 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.802 0 Td [(a)]TJ/F126 7.5716 Tf 4.149 0 Td [(;)]TJ/F123 7.5716 Tf 2.506 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(/)]TJ ET q 1 0 0 1 160.83 346.131 cm []0 d 0 J 0.458 w 0 0 m 20.405 0 l S Q BT /F123 7.5716 Tf 160.925 340.104 Td [(u)]TJ/F126 7.5716 Tf 4.187 0 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(b)]TJ/F126 7.5716 Tf 3.937 0 Td [(;)]TJ/F123 7.5716 Tf 2.507 0 Td 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G 1 0 0 1 -184.612 -98.896 cm BT /F117 9.9626 Tf 184.612 98.896 Td [(.)-307(One)-306(easily)-307(checks)-307(that)]TJ/F126 9.9626 Tf 99.657 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(")]TJ/F117 9.9626 Tf 8.217 -3.616 Td [(satis\002es)-307(condit)1(ions)-307(for)-307(the)-306(weak)]TJ ET 1 0 0 1 45.354 98.896 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -98.896 cm BT /F117 9.9626 Tf 45.354 85.588 Td [(con)40(v)15(er)18(gence)-279(of)]TJ/F126 9.9626 Tf 63.48 0 Td [(.)]TJ/F123 9.9626 Tf 4.484 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 5.105 Td [(")]TJ/F123 7.5716 Tf 0.205 -6.717 Td [(x)]TJ/F126 9.9626 Tf 4.958 1.612 Td [(/)]TJ/F117 9.9626 Tf 6.499 0 Td [(gi)25(v)15(en)-279(in)-280([)]TJ ET 1 0 0 1 181.154 85.588 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -181.154 -85.588 cm BT /F117 9.9626 Tf 181.154 85.588 Td [(3)]TJ ET 1 0 0 1 186.136 85.588 cm 0 g 0 G 1 0 0 1 -186.136 -85.588 cm BT /F117 9.9626 Tf 186.136 85.588 Td [(,)]TJ ET 1 0 0 1 188.626 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7.5716 Tf 9.056 4.115 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F121 9.9626 Tf 7.051 -4.115 Td [(2)]TJ/F117 9.9626 Tf 9.034 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F151 9.9626 Tf 4.942 10.999 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(\013)]TJ/F123 9.9626 Tf 6.774 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 5.105 Td [(")]TJ/F117 7.5716 Tf -1.096 -8.435 Td [(1)]TJ/F126 9.9626 Tf 6.258 3.33 Td [(/)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F126 7.5716 Tf 4.941 4.115 Td [(\013)40(\032)]TJ/F121 7.5716 Tf 8.602 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F123 9.9626 Tf 4.234 -4.115 Td [(q)]TJ/F117 7.5716 Tf 5.031 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(;)]TJ/F117 9.9626 Tf 155.986 0 Td [(\0505.15\051)]TJ ET 1 0 0 1 39.797 570.984 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -570.984 cm BT /F123 9.9626 Tf 39.797 550.421 Td [(wher)37(e)-363(q)]TJ/F123 7.5716 Tf 32.627 -1.494 Td [(t)]TJ/F123 9.9626 Tf 6.951 1.494 Td [(is)-368(the)-368(density)-368(of)-368(the)-368(entr)15(ance)-368(law)-368(of)-368(the)-368(e)20(xcur)10(sion)-368(measur)37(e)-368(of)-368(the)-368(r)37(e\003ected)-368(pr)45(ocess)]TJ ET 1 0 0 1 39.797 550.421 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -550.421 cm BT /F126 9.9626 Tf 39.797 538.466 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F121 9.9626 Tf 9.317 0 Td [(\000)]TJ/F123 9.9626 Tf 10.752 0 Td [(X)]TJ ET q 1 0 0 1 63.582 536.862 cm []0 d 0 J 0.458 w 0 0 m 7.87 0 l S Q BT /F126 9.9626 Tf 71.452 538.466 Td [(;)]TJ/F124 9.9626 Tf 4.958 0 Td [(P)]TJ/F117 7.5716 Tf 6.088 -1.497 Td [(0)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(/)]TJ/F123 9.9626 Tf 3.716 0 Td [(,)-250(wher)37(e)-327(X)]TJ ET q 1 0 0 1 121.949 536.862 cm []0 d 0 J 0.458 w 0 0 m 7.87 0 l S Q BT /F123 7.5716 Tf 129.82 535.796 Td [(t)]TJ/F121 9.9626 Tf 6.052 2.67 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(inf)]TJ/F117 7.5716 Tf 11.068 -1.497 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(t)]TJ/F123 9.9626 Tf 5.712 1.497 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.494 Td [(s)]TJ/F123 9.9626 Tf 3.898 1.494 Td [(.)-250(Mor)37(eo)10(ver)111(,)-250(the)-250(law)-250(of)-467(I)]TJ/F126 9.9626 Tf 96.527 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 3.617 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.617 Td [(/)]TJ/F123 9.9626 Tf 6.207 0 Td [(behaves)-250(as)]TJ ET 1 0 0 1 39.797 538.466 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -538.466 cm BT /F123 9.9626 Tf 64.584 517.257 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F123 9.9626 Tf 4.423 0 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 4.115 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.115 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(\025)]TJ/F123 9.9626 Tf 10.548 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(\030)]TJ/F123 9.9626 Tf 10.499 0 Td [(C)]TJ/F117 7.5716 Tf 6.914 -1.497 Td [(1)]TJ/F123 9.9626 Tf 4.553 1.497 Td [(x)]TJ/F121 7.5716 Tf 5.31 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F126 9.9626 Tf 5.124 -4.115 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(as)-277(x)]TJ/F121 9.9626 Tf 19.693 0 Td [(!)-278(C1)]TJ/F123 9.9626 Tf 31.659 0 Td [(.)]TJ/F117 9.9626 Tf 169.858 0 Td [(\0505.16\051)]TJ ET 1 0 0 1 39.797 517.257 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -517.257 cm BT /F123 9.9626 Tf 39.797 499.03 Td [(If)-473(X)-352(has)-250(positive)-250(jumps,)-250(then)]TJ ET 1 0 0 1 39.797 499.03 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -499.03 cm BT /F123 9.9626 Tf 64.584 478.397 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F123 9.9626 Tf 4.423 0 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 4.114 Td [(")]TJ/F126 9.9626 Tf 5.162 -4.114 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(\024)]TJ/F123 9.9626 Tf 10.548 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(\030)]TJ/F123 9.9626 Tf 10.499 0 Td [(C)]TJ/F117 7.5716 Tf 6.914 -1.498 Td [(2)]TJ/F123 9.9626 Tf 4.553 1.498 Td [(x)]TJ/F126 7.5716 Tf 5.31 4.114 Td [(\013)-40(.\032)]TJ/F121 7.5716 Tf 12.031 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F121 7.5716 Tf 2.824 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(;)]TJ/F123 9.9626 Tf 14.92 0 Td [(as)-277(x)]TJ/F121 9.9626 Tf 19.694 0 Td [(!)]TJ/F117 9.9626 Tf 13.716 0 Td [(0)]TJ/F123 9.9626 Tf 4.982 0 Td [(.)]TJ/F117 9.9626 Tf 159.112 0 Td [(\0505.17\051)]TJ ET 1 0 0 1 39.797 478.397 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -478.397 cm BT /F123 9.9626 Tf 39.797 460.17 Td [(The)-250(constants)-246(C)]TJ/F117 7.5716 Tf 64.438 -1.498 Td [(1)]TJ/F123 9.9626 Tf 6.774 1.498 Td [(and)-273(C)]TJ/F117 7.5716 Tf 24.578 -1.498 Td [(2)]TJ/F123 9.9626 Tf 6.775 1.498 Td [(depend)-250(only)-250(on)]TJ/F126 9.9626 Tf 63.362 0 Td [(\013)]TJ/F123 9.9626 Tf 8.577 0 Td [(and)]TJ/F126 9.9626 Tf 17.704 0 Td [(\032)]TJ/F123 9.9626 Tf 6.027 0 Td [(.)]TJ ET 1 0 0 1 39.797 460.17 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -460.17 cm BT /F117 9.9626 Tf 51.752 441.649 Td [(In)-230(the)-231(case)-230(where)-230(the)-231(process)-230(has)-230(no)-231(positi)25(v)15(e)-230(jumps,)-230(the)-231(la)15(w)-230(of)]TJ/F123 9.9626 Tf 250.503 0 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 3.616 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.616 Td [(/)]TJ/F117 9.9626 Tf 6.011 0 Td [(is)-230(gi)25(v)15(en)-231(e)15(xplicitly)-230(in)-230(the)]TJ ET 1 0 0 1 39.797 441.649 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -441.649 cm BT /F117 9.9626 Tf 39.797 429.694 Td [(ne)15(xt)-250(theorem.)]TJ ET 1 0 0 1 39.797 429.694 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -19.223 cm 0 g 0 G 1 0 0 1 -35.812 -410.471 cm BT /F124 9.9626 Tf 39.797 410.471 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 65.75 410.471 cm 0 g 0 G 1 0 0 1 -65.75 -410.471 cm BT /F117 9.9626 Tf 69.735 410.471 Td [(Let)]TJ/F123 9.9626 Tf 15.598 0 Td [(n)]TJ/F117 9.9626 Tf 7.748 0 Td [(be)-233(the)-232(measure)-233(of)-233(the)-232(e)15(xcursions)-233(a)15(w)10(ay)-233(form)-232(0)-233(of)-233(the)-232(re\003ected)-233(process)]TJ/F123 9.9626 Tf 278.383 0 Td [(X)]TJ/F121 9.9626 Tf 8.679 0 Td [(\000)]TJ/F123 9.9626 Tf 10.113 0 Td [(X)]TJ ET q 1 0 0 1 389.489 408.867 cm []0 d 0 J 0.458 w 0 0 m 7.87 0 l S Q BT /F117 9.9626 Tf 399.677 410.471 Td [(under)]TJ ET 1 0 0 1 39.797 410.471 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -410.471 cm BT /F124 9.9626 Tf 39.797 398.515 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.497 Td [(0)]TJ/F117 9.9626 Tf 4.284 1.497 Td [(.)-331(It)-330(is)-331(pro)15(v)15(ed)-330(in)-330([)]TJ ET 1 0 0 1 120.288 398.515 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -120.288 -398.515 cm BT /F117 9.9626 Tf 120.288 398.515 Td [(23)]TJ ET 1 0 0 1 130.251 398.515 cm 0 g 0 G 1 0 0 1 -130.251 -398.515 cm BT /F117 9.9626 Tf 130.251 398.515 Td [(])-330(that)-331(the)-330(entrance)-330(la)15(w)-331(of)]TJ/F123 9.9626 Tf 106.463 0 Td [(n)]TJ/F117 9.9626 Tf 8.721 0 Td [(is)-330(absolutely)-331(continuous)-330(with)-330(respect)-331(to)-330(the)]TJ ET 1 0 0 1 39.797 398.515 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -398.515 cm BT /F117 9.9626 Tf 39.797 386.56 Td [(Lebesgue)-271(measure.)-271(Let)-271(us)-271(denote)-271(by)]TJ/F123 9.9626 Tf 148.67 0 Td [(q)]TJ/F123 7.5716 Tf 5.031 -1.494 Td [(t)]TJ/F117 9.9626 Tf 5.984 1.494 Td [(its)-271(density)65(.)-271(Then)-271(from)-271([)]TJ ET 1 0 0 1 293.479 386.56 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -293.479 -386.56 cm BT /F117 9.9626 Tf 293.479 386.56 Td [(12)]TJ ET 1 0 0 1 303.441 386.56 cm 0 g 0 G 1 0 0 1 -303.441 -386.56 cm BT /F117 9.9626 Tf 303.441 386.56 Td [(],)-271(the)-271(entrance)-271(la)15(w)-271(of)]TJ/F126 9.9626 Tf 87.759 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 3.617 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.617 Td [(/)]TJ ET 1 0 0 1 39.797 386.56 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -386.56 cm BT /F117 9.9626 Tf 39.797 374.605 Td [(is)-250(related)-250(to)]TJ/F123 9.9626 Tf 48.926 0 Td [(q)]TJ/F117 7.5716 Tf 5.031 -1.497 Td [(1)]TJ/F117 9.9626 Tf 6.774 1.497 Td [(by)]TJ ET 1 0 0 1 39.797 374.605 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -374.605 cm BT /F34 9.9626 Tf 63.707 356.378 Td [(P)]TJ/F121 7.5716 Tf 6.088 4.115 Td [(")]TJ/F126 9.9626 Tf 5.163 -4.115 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F117 7.5716 Tf 6.804 -1.497 Td [(1)]TJ/F121 9.9626 Tf 7.052 1.497 Td [(2)]TJ/F117 9.9626 Tf 9.033 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 11.176 0 Td [(y)]TJ/F126 7.5716 Tf 4.941 4.115 Td [(\013)40(\032)]TJ/F123 9.9626 Tf 9.05 -4.115 Td [(q)]TJ/F117 7.5716 Tf 5.031 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(;)]TJ/F123 9.9626 Tf 15.558 0 Td [(y)]TJ/F121 9.9626 Tf 7.709 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(:)]TJ ET 1 0 0 1 39.797 356.378 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -356.378 cm BT /F117 9.9626 Tf 39.797 338.151 Td [(W)80(e)-250(readily)-250(deri)25(v)15(e)]TJ ET 1 0 0 1 112.464 338.151 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -112.464 -338.151 cm BT /F117 9.9626 Tf 112.464 338.151 Td [(\0505.15\051)]TJ ET 1 0 0 1 136.533 338.151 cm 0 g 0 G 1 0 0 1 -136.533 -338.151 cm BT /F117 9.9626 Tf 139.024 338.151 Td [(from)-250(identity)]TJ ET 1 0 0 1 193.818 338.151 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -193.818 -338.151 cm BT /F117 9.9626 Tf 193.818 338.151 Td [(\0505.14\051)]TJ ET 1 0 0 1 217.888 338.151 cm 0 g 0 G 1 0 0 1 -217.888 -338.151 cm BT /F117 9.9626 Tf 217.888 338.151 Td [(.)-250(Moreo)15(v)15(er)-250(from)-250(\0503.18\051)-250(in)-250([)]TJ ET 1 0 0 1 326.32 338.151 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -326.32 -338.151 cm BT /F117 9.9626 Tf 326.32 338.151 Td [(23)]TJ ET 1 0 0 1 336.283 338.151 cm 0 g 0 G 1 0 0 1 -336.283 -338.151 cm BT /F117 9.9626 Tf 336.283 338.151 Td [(]:)]TJ ET 1 0 0 1 39.797 338.151 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -338.151 cm BT /F151 9.9626 Tf 63.707 328.204 Td [(Z)]TJ/F123 7.5716 Tf 10.028 -2.922 Td [(x)]TJ/F117 7.5716 Tf -4.768 -19.593 Td [(0)]TJ/F123 9.9626 Tf 10.912 8.956 Td [(q)]TJ/F117 7.5716 Tf 5.031 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.)]TJ/F123 9.9626 Tf 4.354 0 Td [(y)]TJ/F126 9.9626 Tf 4.941 0 Td [(/)]TJ/F117 9.9626 Tf 5.377 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 7.709 0 Td [(\030)]TJ/F123 9.9626 Tf 10.498 0 Td [(C)-114(x)]TJ/F126 7.5716 Tf 13.091 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(1)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\032)-60(/)]TJ/F121 7.5716 Tf 7.405 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(;)]TJ/F117 9.9626 Tf 14.92 0 Td [(as)]TJ/F123 9.9626 Tf 11.059 0 Td [(x)]TJ/F121 9.9626 Tf 8.077 0 Td [(!)]TJ/F117 9.9626 Tf 13.716 0 Td [(0,)]TJ ET 1 0 0 1 39.797 314.645 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -314.645 cm BT /F117 9.9626 Tf 39.797 291.52 Td [(and)-250(from)-250(\0503.20\051)-250(of)-250(the)-250(same)-250(paper)40(,)-250(if)]TJ/F123 9.9626 Tf 149.767 0 Td [(X)]TJ/F117 9.9626 Tf 9.594 0 Td [(has)-250(positi)25(v)15(e)-250(jumps,)-250(then:)]TJ ET 1 0 0 1 39.797 291.52 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -291.52 cm BT /F151 9.9626 Tf 63.707 281.482 Td [(Z)]TJ/F121 7.5716 Tf 9.823 -2.922 Td [(1)]TJ/F123 7.5716 Tf -4.358 -19.593 Td [(x)]TJ/F123 9.9626 Tf 14.198 8.956 Td [(q)]TJ/F117 7.5716 Tf 5.031 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(.)]TJ/F123 9.9626 Tf 4.353 0 Td [(y)]TJ/F126 9.9626 Tf 4.942 0 Td [(/)]TJ/F117 9.9626 Tf 5.376 0 Td [(d)]TJ/F123 9.9626 Tf 5.619 0 Td [(y)]TJ/F121 9.9626 Tf 7.709 0 Td [(\030)]TJ/F123 9.9626 Tf 10.498 0 Td [(C)]TJ/F121 7.5716 Tf 7.512 4.115 Td [(0)]TJ/F123 9.9626 Tf 2.812 -4.115 Td [(x)]TJ/F121 7.5716 Tf 5.31 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F126 9.9626 Tf 5.124 -4.115 Td [(;)]TJ/F117 9.9626 Tf 14.921 0 Td [(as)]TJ/F123 9.9626 Tf 11.058 0 Td [(x)]TJ/F121 9.9626 Tf 8.077 0 Td [(!)-278(C1)]TJ/F117 9.9626 Tf 31.659 0 Td [(.)]TJ ET 1 0 0 1 39.797 267.923 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -267.923 cm BT /F117 9.9626 Tf 39.797 243.926 Td [(This)-241(together)-241(with)]TJ ET 1 0 0 1 115.068 243.926 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -115.068 -243.926 cm BT /F117 9.9626 Tf 115.068 243.926 Td [(\0505.14\051)]TJ ET 1 0 0 1 139.138 243.926 cm 0 g 0 G 1 0 0 1 -139.138 -243.926 cm BT /F117 9.9626 Tf 141.537 243.926 Td [(imply)]TJ ET 1 0 0 1 167.189 243.926 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -167.189 -243.926 cm BT /F117 9.9626 Tf 167.189 243.926 Td [(\0505.16\051)]TJ ET 1 0 0 1 191.259 243.926 cm 0 g 0 G 1 0 0 1 -191.259 -243.926 cm BT /F117 9.9626 Tf 193.658 243.926 Td [(and)]TJ ET 1 0 0 1 210.443 243.926 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -210.443 -243.926 cm BT /F117 9.9626 Tf 210.443 243.926 Td [(\0505.17\051)]TJ ET 1 0 0 1 234.513 243.926 cm 0 g 0 G 1 0 0 1 -234.513 -243.926 cm BT /F117 9.9626 Tf 234.513 243.926 Td [(.)-241(The)-241(constants)]TJ/F123 9.9626 Tf 62.221 0 Td [(C)]TJ/F117 9.9626 Tf 9.911 0 Td [(and)]TJ/F123 9.9626 Tf 16.746 0 Td [(C)]TJ/F121 7.5716 Tf 7.511 3.616 Td [(0)]TJ/F117 9.9626 Tf 4.942 -3.616 Td [(depend)-241(only)-241(on)]TJ/F126 9.9626 Tf 63.646 0 Td [(\013)]TJ/F117 9.9626 Tf 8.486 0 Td [(and)]TJ ET 1 0 0 1 39.797 243.926 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -243.926 cm BT /F126 9.9626 Tf 39.797 231.97 Td [(\032)]TJ/F117 9.9626 Tf 6.027 0 Td [(.)]TJ/F116 9.9626 Tf 17.435 0 Td [(\004)]TJ ET 1 0 0 1 39.797 231.97 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -231.97 cm BT /F117 9.9626 Tf 51.752 213.45 Td [(Another)-412(w)10(ay)-412(to)-412(pro)15(v)15(e)-411(part)-412(\050i\051)-412(of)-412(this)-412(theorem)-412(is)-411(to)-412(use)-412(a)-412(result)-412(due)-412(to)-411(M)]TJ 310.952 0.049 Td [(\264)]TJ -0.553 -0.049 Td [(ejane)-412([)]TJ ET 1 0 0 1 390.593 213.45 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -390.593 -213.45 cm BT /F117 9.9626 Tf 390.593 213.45 Td [(22)]TJ ET 1 0 0 1 400.556 213.45 cm 0 g 0 G 1 0 0 1 -400.556 -213.45 cm BT /F117 9.9626 Tf 400.556 213.45 Td [(])-412(and)]TJ ET 1 0 0 1 39.797 213.45 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -213.45 cm BT /F117 9.9626 Tf 39.797 201.494 Td [(Ri)25(v)15(ero)-384([)]TJ ET 1 0 0 1 73.664 201.494 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -73.664 -201.494 cm BT /F117 9.9626 Tf 73.664 201.494 Td [(26)]TJ ET 1 0 0 1 83.627 201.494 cm 0 g 0 G 1 0 0 1 -83.627 -201.494 cm BT /F117 9.9626 Tf 83.627 201.494 Td [(])-384(which)-385(asserts)-384(that)-385(for)-384(a)-385(non-arithmetic)-384(L)]TJ 177.319 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-384(process)]TJ/F126 9.9626 Tf 51.924 0 Td [(\030)]TJ/F117 9.9626 Tf 5.34 0 Td [(,)-385(if)-384(Cramer')55(s)-384(condition)-385(is)]TJ ET 1 0 0 1 39.797 201.494 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -201.494 cm BT /F117 9.9626 Tf 39.797 189.539 Td [(satis\002ed)-268(for)]TJ/F126 9.9626 Tf 49.619 0 Td [(\022)-412(>)]TJ/F117 9.9626 Tf 19.36 0 Td [(0,)-268(i.e.)]TJ/F123 9.9626 Tf 25.68 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(e)15(xp)]TJ/F126 9.9626 Tf 15.897 0 Td [(\022)-100(\030)]TJ/F117 7.5716 Tf 9.624 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(/)]TJ/F121 9.9626 Tf 6.821 0 Td [(D)]TJ/F117 9.9626 Tf 10.875 0 Td [(1)-268(and)]TJ/F123 9.9626 Tf 25.401 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 4.295 Td [(C)]TJ/F117 7.5716 Tf -1.096 -7.625 Td [(1)]TJ/F117 9.9626 Tf 9.16 3.33 Td [(e)15(xp)]TJ/F126 9.9626 Tf 15.897 0 Td [(\022)-100(\030)]TJ/F117 7.5716 Tf 9.624 -1.497 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.497 Td [(/)-312(<)]TJ/F121 9.9626 Tf 17.696 0 Td [(1)]TJ/F117 9.9626 Tf 10.172 0 Td [(,)-268(then)]TJ/F123 9.9626 Tf 25.869 0 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F123 9.9626 Tf 4.423 0 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)-110(/)]TJ/F121 9.9626 Tf 15.877 0 Td [(\025)]TJ/F123 9.9626 Tf 10.885 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.821 0 Td [(\030)]TJ/F123 9.9626 Tf 10.836 0 Td [(C)-114(x)]TJ/F121 7.5716 Tf 13.091 3.617 Td [(\000)]TJ/F126 7.5716 Tf 5.905 0 Td [(\013)-40(\022)]TJ/F117 9.9626 Tf 9.213 -3.617 Td [(.)]TJ ET 1 0 0 1 39.797 189.539 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -189.539 cm BT /F117 9.9626 Tf 39.797 177.584 Td [(These)-428(ar)18(guments)-429(and)]TJ ET 1 0 0 1 132.104 177.584 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -132.104 -177.584 cm BT /F117 9.9626 Tf 132.104 177.584 Td [(Proposition)-428(1)]TJ ET 1 0 0 1 187.301 177.584 cm 0 g 0 G 1 0 0 1 -187.301 -177.584 cm BT /F117 9.9626 Tf 191.569 177.584 Td 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0 1 45.354 522.015 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -522.015 cm BT /F123 9.9626 Tf 70.141 499.301 Td [(P)]TJ/F126 9.9626 Tf 6.904 0 Td [(.)]TJ/F123 9.9626 Tf 4.424 0 Td [(I)]TJ/F126 9.9626 Tf 4.901 0 Td [(.)]TJ/F121 9.9626 Tf 3.717 0 Td [(\000)]TJ/F126 9.9626 Tf 7.77 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 4.115 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -4.115 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(\024)]TJ/F123 9.9626 Tf 10.548 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(\030)]TJ/F123 9.9626 Tf 11.734 6.984 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ ET q 1 0 0 1 148.199 501.792 cm []0 d 0 J 0.458 w 0 0 m 10.827 0 l S Q BT /F126 9.9626 Tf 150.569 492.228 Td [(\013)]TJ/F123 9.9626 Tf 9.922 7.073 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(as)-277(x)]TJ/F121 9.9626 Tf 19.693 0 Td [(!)]TJ/F117 9.9626 Tf 13.717 0 Td [(0)]TJ/F123 9.9626 Tf 4.981 0 Td [(.)]TJ/F117 9.9626 Tf 184.737 0 Td [(\0505.19\051)]TJ ET 1 0 0 1 45.354 499.301 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -499.301 cm BT /F117 9.9626 Tf 45.354 471.792 Td [(In)-323(the)-323(remainder)-322(of)-323(this)-323(section,)-323(we)-323(assume)-322(that)]TJ/F126 9.9626 Tf 199.105 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F123 7.5716 Tf 6.293 -1.494 Td [(x)]TJ/F126 9.9626 Tf 4.533 1.494 Td [(/)]TJ/F117 9.9626 Tf 6.932 0 Td [(has)-323(no)-323(positi)25(v)15(e)-322(jumps)-323(and)-323(recall)-323(that)]TJ ET 1 0 0 1 45.354 471.792 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -471.792 cm BT /F123 9.9626 Tf 45.354 459.837 Td [(m)]TJ/F121 9.9626 Tf 10.548 0 Td [(D)]TJ/F123 9.9626 Tf 11.226 0 Td [(E)]TJ/F126 9.9626 Tf 6.984 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 3.617 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.617 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(.)]TJ ET 1 0 0 1 45.354 459.837 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -21.982 cm 0 g 0 G 1 0 0 1 -41.369 -437.855 cm BT /F124 9.9626 Tf 45.354 437.855 Td [(Theor)18(em)-250(7.)]TJ ET 1 0 0 1 93.872 437.855 cm 0 g 0 G 1 0 0 1 -93.872 -437.855 cm BT /F123 9.9626 Tf 97.857 437.855 Td [(The)-422(law)-422(of)-422(e)20(xponential)-422(functional)-493(I)]TJ/F126 9.9626 Tf 150.42 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 3.617 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.617 Td [(/)]TJ/F121 9.9626 Tf 9.655 0 Td [(D)]TJ/F151 9.9626 Tf 13.71 8.025 Td [(R)]TJ/F121 7.5716 Tf 6.495 -2.923 Td [(1)]TJ/F117 7.5716 Tf -1.933 -8.524 Td [(0)]TJ/F117 9.9626 Tf 11.822 3.422 Td [(e)15(xp)]TJ/F121 9.9626 Tf 14.237 0 Td [(f\000)]TJ/F126 9.9626 Tf 11.457 0 Td [(\013)-40(\030)]TJ/F121 7.5716 Tf 11.427 5.105 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F123 7.5716 Tf -8.266 -6.717 Td [(s)]TJ/F121 9.9626 Tf 12.55 1.612 Td [(g)]TJ/F117 9.9626 Tf 5.347 0 Td [(d)]TJ/F123 9.9626 Tf 4.981 0 Td [(s)-482(is)-422(absolutely)]TJ ET 1 0 0 1 45.354 437.855 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -437.855 cm BT /F123 9.9626 Tf 45.354 424.664 Td [(continuous)-347(wit)1(h)-347(r)37(espect)-346(to)-347(the)-346(Lebesgue)-347(measur)37(e)-346(and)-347(has)-346(a)-347(continuous)-346(density)-462(p)]TJ/F121 7.5716 Tf 333.806 3.617 Td [(")]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.617 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\001)]TJ/F126 9.9626 Tf 2.769 0 Td [(/)]TJ/F123 9.9626 Tf 7.169 0 Td [(whic)15(h)]TJ ET 1 0 0 1 45.354 424.664 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -424.664 cm BT /F123 9.9626 Tf 45.354 412.709 Td [(has)-250(the)-250(following)-250(r)37(epr)37(esentation)-250(by)-250(power)-250(series)]TJ ET 1 0 0 1 45.354 412.709 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -412.709 cm BT /F123 9.9626 Tf 70.41 387.294 Td [(p)]TJ/F121 7.5716 Tf 5.291 4.114 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 19.505 6.983 Td [(c)]TJ/F121 7.5716 Tf 4.622 3.617 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET q 1 0 0 1 122.438 389.784 cm []0 d 0 J 0.458 w 0 0 m 14.812 0 l S Q BT /F126 9.9626 Tf 123.568 380.22 Td [(\031)]TJ/F123 9.9626 Tf 7.242 0 Td [(x)]TJ/F121 7.5716 Tf 12.479 18.641 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.103 Td [(X)]TJ/F123 7.5716 Tf 0.14 -20.882 Td [(n)]TJ/F121 7.5716 Tf 4.126 0 Td [(D)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F40 9.9626 Tf 5.586 11.418 Td [(\000)]TJ/F151 9.9626 Tf 9.234 10.998 Td [(\020)]TJ/F117 9.9626 Tf 5.43 -10.998 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F123 9.9626 Tf 11.509 6.983 Td [(n)]TJ ET q 1 0 0 1 188.903 389.784 cm []0 d 0 J 0.458 w 0 0 m 6.087 0 l S Q BT /F126 9.9626 Tf 188.903 380.22 Td [(\013)]TJ/F151 9.9626 Tf 7.283 18.072 Td [(\021)]TJ/F117 9.9626 Tf 7.09 -10.998 Td [(sin)]TJ/F151 9.9626 Tf 13.287 10.998 Td [(\020)]TJ/F126 9.9626 Tf 6.625 -4.015 Td [(\031)]TJ/F123 9.9626 Tf 6.974 0 Td [(n)]TJ ET q 1 0 0 1 223.188 389.784 cm []0 d 0 J 0.458 w 0 0 m 12.403 0 l S Q BT /F126 9.9626 Tf 226.346 380.22 Td [(\013)]TJ/F151 9.9626 Tf 10.441 18.072 Td [(\021)]TJ/F126 9.9626 Tf 8.285 -4.015 Td [(.)]TJ/F121 9.9626 Tf 3.717 0 Td [(\000)]TJ/F123 9.9626 Tf 8.039 0 Td [(x)]TJ/F121 7.5716 Tf 5.31 3.617 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F126 9.9626 Tf 8.683 -3.617 Td [(/)]TJ/F123 7.5716 Tf 3.716 3.617 Td [(n)]TJ ET q 1 0 0 1 245.072 389.784 cm []0 d 0 J 0.458 w 0 0 m 43.781 0 l S Q BT /F123 9.9626 Tf 262.868 380.22 Td [(n)]TJ/F121 9.9626 Tf 5.43 0 Td [(W)]TJ/F126 9.9626 Tf 21.751 7.074 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(for)-300(x)]TJ/F126 9.9626 Tf 22.692 0 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ ET 1 0 0 1 45.354 387.294 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -387.294 cm BT /F123 9.9626 Tf 45.354 358.727 Td [(wher)37(e)-250(c)]TJ/F121 9.9626 Tf 33.861 0 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ/F40 9.9626 Tf 6.404 1.494 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(2)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)-40(/\013)]TJ/F121 7.5716 Tf 15.89 3.617 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -3.617 Td [(.\013)]TJ/F121 9.9626 Tf 12.017 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 3.617 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 7.051 -3.617 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F123 9.9626 Tf 4.982 0 Td [(.)]TJ ET 1 0 0 1 45.354 358.727 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -358.727 cm BT /F123 9.9626 Tf 57.31 346.685 Td [(Mor)37(eo)10(ver)-250(the)-250(positive)-250(entir)37(e)-250(moments)-250(of)]TJ/F126 9.9626 Tf 164.421 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.755 0 Td [(;)]TJ/F34 9.9626 Tf 4.958 0 Td [(P)]TJ/F121 7.5716 Tf 6.088 3.617 Td [(")]TJ/F126 9.9626 Tf 5.162 -3.617 Td [(/)]TJ/F123 9.9626 Tf 3.716 0 Td [(,)-250(for)-273(t)]TJ/F126 9.9626 Tf 25.761 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F123 9.9626 Tf 4.982 0 Td [(,)-250(ar)37(e)-250(given)-250(by)-250(the)-250(identity)]TJ ET 1 0 0 1 45.354 346.685 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -346.685 cm BT /F34 9.9626 Tf 69.265 321.66 Td [(E)]TJ/F121 7.5716 Tf 6.641 4.114 Td [(")]TJ/F151 9.9626 Tf 6.823 6.885 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -11.064 Td [(.)]TJ/F123 9.9626 Tf 4.483 0.065 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.495 Td [(t)]TJ/F126 9.9626 Tf 3.285 1.43 Td [(/)]TJ/F123 7.5716 Tf 3.716 4.179 Td [(k)]TJ/F151 9.9626 Tf 4.314 6.885 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(m)-59(t)]TJ/F126 9.9626 Tf 11.447 0 Td [(/)]TJ/F123 7.5716 Tf 3.716 4.114 Td [(k)]TJ/F40 9.9626 Tf 5.51 2.87 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(.)]TJ/F123 9.9626 Tf 13.52 0 Td [(k)]TJ/F121 9.9626 Tf 7.235 0 Td [(C)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(//)]TJ ET q 1 0 0 1 153.885 324.15 cm []0 d 0 J 0.458 w 0 0 m 50.727 0 l S Q BT /F40 9.9626 Tf 154.984 314.466 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.\013)-40(/)]TJ/F126 7.5716 Tf 13.519 2.879 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(k)]TJ/F121 7.5716 Tf 3.816 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F123 9.9626 Tf 3.322 -2.879 Td [(k)]TJ/F121 9.9626 Tf 5.021 0 Td [(W)]TJ/F126 9.9626 Tf 5.054 7.194 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(k)]TJ/F121 9.9626 Tf 7.789 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F117 9.9626 Tf 160.073 0 Td [(\0505.20\051)]TJ ET 1 0 0 1 45.354 321.66 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -321.66 cm BT /F123 9.9626 Tf 45.354 298.765 Td [(and)-258(its)-257(law)-258(is)-257(absolutely)-258(continuous)-257(with)-258(r)37(espect)-257(to)-258(the)-257(Lebesgue)-258(measur)37(e)-258(and)-257(has)-258(a)-257(continuous)]TJ ET 1 0 0 1 45.354 298.765 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -298.765 cm BT /F123 9.9626 Tf 45.354 286.81 Td [(density)-365(p)]TJ/F123 7.5716 Tf 36.852 -1.494 Td [(t)]TJ/F126 9.9626 Tf 3.284 1.494 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\001)]TJ/F126 9.9626 Tf 2.77 0 Td [(/)]TJ/F123 9.9626 Tf 6.207 0 Td [(whic)15(h)-250(has)-250(the)-250(following)-250(r)37(epr)37(esentation)-250(by)-250(power)-250(series)]TJ ET 1 0 0 1 45.354 286.81 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -286.81 cm BT /F123 9.9626 Tf 70.41 261.395 Td [(p)]TJ/F123 7.5716 Tf 4.992 -1.495 Td [(t)]TJ/F126 9.9626 Tf 3.284 1.495 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 25.062 6.984 Td [(t)]TJ/F121 7.5716 Tf 3.666 3.616 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F126 9.9626 Tf 8.683 -3.616 Td [(.\013)]TJ/F121 9.9626 Tf 12.017 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ ET q 1 0 0 1 113.969 263.885 cm []0 d 0 J 0.458 w 0 0 m 63.856 0 l S Q BT /F40 9.9626 Tf 113.969 254.321 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F117 9.9626 Tf 3.717 0 Td [(2)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.984 0 Td [(\013)-40(/)]TJ/F123 9.9626 Tf 9.804 0 Td [(c)]TJ/F121 7.5716 Tf 4.423 -1.494 Td [(\000)]TJ/F123 9.9626 Tf 6.404 1.494 Td [(m)]TJ/F126 9.9626 Tf 7.781 0 Td [(\031)]TJ/F121 7.5716 Tf 13.013 18.641 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.103 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.882 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F40 9.9626 Tf 5.586 11.418 Td [(\000)]TJ/F151 9.9626 Tf 9.235 10.998 Td [(\020)]TJ/F117 9.9626 Tf 5.429 -10.998 Td [(1)]TJ/F121 9.9626 Tf 7.196 0 Td [(C)]TJ/F123 9.9626 Tf 11.509 6.984 Td [(n)]TJ ET q 1 0 0 1 229.478 263.885 cm []0 d 0 J 0.458 w 0 0 m 6.087 0 l S Q BT /F126 9.9626 Tf 229.478 254.321 Td [(\013)]TJ/F151 9.9626 Tf 7.283 18.072 Td [(\021)]TJ/F117 9.9626 Tf 7.09 -10.998 Td [(sin)]TJ/F151 9.9626 Tf 13.286 10.998 Td [(\020)]TJ/F126 9.9626 Tf 6.625 -4.015 Td [(\031)]TJ/F123 9.9626 Tf 6.974 0 Td [(n)]TJ ET q 1 0 0 1 263.762 263.885 cm []0 d 0 J 0.458 w 0 0 m 12.403 0 l S Q BT /F126 9.9626 Tf 266.921 254.321 Td [(\013)]TJ/F151 9.9626 Tf 10.44 18.072 Td [(\021)]TJ/F126 9.9626 Tf 8.286 -4.015 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 8.04 0 Td [(x)]TJ/F117 7.5716 Tf 5.31 3.617 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F126 9.9626 Tf 8.683 -3.617 Td [(/)]TJ/F123 7.5716 Tf 3.716 3.617 Td [(n)]TJ ET q 1 0 0 1 285.647 263.885 cm []0 d 0 J 0.458 w 0 0 m 37.876 0 l S Q BT /F123 9.9626 Tf 300.49 254.321 Td [(n)]TJ/F121 9.9626 Tf 5.43 0 Td [(W)]TJ/F126 9.9626 Tf 18.798 7.074 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(for)-300(x)]TJ/F126 9.9626 Tf 22.692 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(:)]TJ ET 1 0 0 1 45.354 261.395 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -33.798 cm 0 g 0 G 1 0 0 1 -41.369 -227.597 cm BT /F124 9.9626 Tf 45.354 227.597 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 71.307 227.597 cm 0 g 0 G 1 0 0 1 -71.307 -227.597 cm BT /F117 9.9626 Tf 75.292 227.597 Td [(From)-261(Bertoin)-261(and)-261(Y)110(or)-260([)]TJ ET 1 0 0 1 169.264 227.597 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -169.264 -227.597 cm BT /F117 9.9626 Tf 169.264 227.597 Td [(5)]TJ ET 1 0 0 1 174.245 227.597 cm 0 g 0 G 1 0 0 1 -174.245 -227.597 cm BT /F117 9.9626 Tf 174.245 227.597 Td [(],)-261(we)-261(kno)25(w)-261(that)-261(the)-260(distrib)20(ution)-261(of)-261(the)-261(e)15(xponential)-261(functional)-261(of)]TJ ET 1 0 0 1 45.354 227.597 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -227.597 cm BT /F117 9.9626 Tf 45.354 215.642 Td [(a)-321(spectrally)-322(ne)15(g)5(ati)25(v)15(e)-321(L)]TJ 92.559 0.049 Td [(\264)]TJ -0.553 -0.049 Td [(evy)-321(process)-322(is)-321(determined)-321(by)-322(its)-321(ne)15(g)5(ati)25(v)15(e)-322(entire)-321(moments.)-322(In)-321(particular)40(,)]TJ ET 1 0 0 1 45.354 215.642 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -215.642 cm BT /F117 9.9626 Tf 45.354 203.686 Td [(the)-250(e)15(xponential)-250(functional)-250(for)]TJ/F126 9.9626 Tf 120.487 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.617 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.507 0 Td [(n)]TJ/F117 9.9626 Tf 6.774 -3.617 Td [(satis\002es)]TJ ET 1 0 0 1 45.354 203.686 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -203.686 cm BT /F123 9.9626 Tf 69.952 178.561 Td [(E)]TJ/F151 9.9626 Tf 8.644 10.999 Td [(\020)]TJ/F123 9.9626 Tf 6.137 -10.999 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 4.115 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(/)]TJ/F121 7.5716 Tf 3.716 4.115 Td [(\000)]TJ/F123 7.5716 Tf 5.906 0 Td [(k)]TJ/F151 9.9626 Tf 4.314 6.884 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(m)]TJ/F123 7.5716 Tf 7.781 4.115 Td [(k)]TJ/F40 9.9626 Tf 21.353 2.869 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(k)]TJ/F126 9.9626 Tf 5.021 0 Td [(\013)-40(/)]TJ ET q 1 0 0 1 162.194 181.052 cm []0 d 0 J 0.458 w 0 0 m 57.801 0 l S Q BT /F40 9.9626 Tf 162.194 171.488 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(/)]TJ/F123 7.5716 Tf 13.52 2.879 Td [(k)]TJ/F126 9.9626 Tf 4.314 -2.879 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(k)]TJ/F121 9.9626 Tf 7.235 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 9.9626 Tf 3.716 0 Td [(W)]TJ/F126 9.9626 Tf 3.955 7.073 Td [(;)]TJ/F117 9.9626 Tf 182.66 0 Td [(\0505.21\051)]TJ ET 1 0 0 1 45.354 178.561 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -178.561 cm BT /F117 9.9626 Tf 45.354 155.812 Td [(with)-285(the)-285(con)40(v)15(ention)-286(that)-285(the)-285(right-hand)-285(side)-285(equals)]TJ/F126 9.9626 Tf 206.471 0 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(m)]TJ/F117 9.9626 Tf 10.622 0 Td [(for)]TJ/F123 9.9626 Tf 14.458 0 Td [(k)]TJ/F121 9.9626 Tf 8.438 0 Td [(D)]TJ/F117 9.9626 Tf 11.188 0 Td [(1.)-285(In)-286(particular)40(,)-285(from)]TJ ET 1 0 0 1 389.392 155.812 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -389.392 -155.812 cm BT /F117 9.9626 Tf 389.392 155.812 Td [(\0505.14\051)]TJ ET 1 0 0 1 413.462 155.812 cm 0 g 0 G 1 0 0 1 -413.462 -155.812 cm BT /F117 9.9626 Tf 416.303 155.812 Td [(we)]TJ ET 1 0 0 1 45.354 155.812 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -155.812 cm BT /F117 9.9626 Tf 45.354 143.857 Td [(ha)20(v)15(e)-250(that)]TJ ET 1 0 0 1 45.354 143.857 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -143.857 cm BT /F34 9.9626 Tf 69.265 122.742 Td [(E)]TJ/F121 7.5716 Tf 6.641 4.115 Td [(")]TJ/F151 9.9626 Tf 6.823 6.884 Td [(\020)]TJ/F126 9.9626 Tf 5.43 -11.064 Td [(.)]TJ/F123 9.9626 Tf 4.483 0.065 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.494 Td [(t)]TJ/F126 9.9626 Tf 3.285 1.429 Td [(/)]TJ/F123 7.5716 Tf 3.716 4.18 Td [(k)]TJ/F151 9.9626 Tf 4.314 6.884 Td [(\021)]TJ/F121 9.9626 Tf 8.197 -10.999 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(.)]TJ/F123 9.9626 Tf 3.716 0 Td [(m)-59(t)]TJ/F126 9.9626 Tf 11.447 0 Td [(/)]TJ/F123 7.5716 Tf 3.716 4.115 Td [(k)]TJ/F40 9.9626 Tf 5.51 2.869 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)-40(.)]TJ/F123 9.9626 Tf 13.52 0 Td [(k)]TJ/F121 9.9626 Tf 7.235 0 Td [(C)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(//)]TJ ET q 1 0 0 1 153.885 125.233 cm []0 d 0 J 0.458 w 0 0 m 50.727 0 l S Q BT /F40 9.9626 Tf 154.984 115.548 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.\013)-40(/)]TJ/F126 7.5716 Tf 13.519 2.879 Td [(.)]TJ/F123 7.5716 Tf 2.824 0 Td [(k)]TJ/F121 7.5716 Tf 3.816 0 Td [(C)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(/)]TJ/F123 9.9626 Tf 3.322 -2.879 Td [(k)]TJ/F121 9.9626 Tf 5.021 0 Td [(W)]TJ/F126 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15.649 0 Td [(D)]TJ/F126 9.9626 Tf 10.538 0 Td [(\025)]TJ/F126 7.5716 Tf 5.45 3.616 Td [(\014)]TJ/F117 9.9626 Tf 5.298 -3.616 Td [(,)-250(is)-250(gi)25(v)15(en)-250(by)]TJ ET 1 0 0 1 39.797 559.886 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -559.886 cm BT /F126 9.9626 Tf 63.707 532.044 Td [(\032)]TJ/F123 7.5716 Tf 5.43 -1.495 Td [(t)]TJ/F126 9.9626 Tf 3.284 1.495 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)-167(\014)-70(/)]TJ/F121 9.9626 Tf 17.758 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 19.505 6.983 Td [(t)]TJ/F121 7.5716 Tf 3.666 3.617 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\014)]TJ ET q 1 0 0 1 118.979 534.534 cm []0 d 0 J 0.458 w 0 0 m 22.215 0 l S Q BT /F126 9.9626 Tf 123.81 524.97 Td [(\031)]TJ/F123 9.9626 Tf 7.243 0 Td [(x)]TJ/F121 7.5716 Tf 16.18 18.641 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.103 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.882 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F40 9.9626 Tf 5.585 11.418 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F123 9.9626 Tf 9.985 0 Td [(n)]TJ/F126 9.9626 Tf 4.732 0 Td [(\014)-70(/)]TJ/F117 9.9626 Tf 11.693 0 Td [(sin)]TJ/F126 9.9626 Tf 11.626 0 Td [(.\014)-70(\031)]TJ/F123 9.9626 Tf 17.006 0 Td [(n)]TJ/F126 9.9626 Tf 5.43 0 Td [(/)]TJ 4.911 6.983 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 8.04 0 Td [(x)]TJ/F121 7.5716 Tf 5.31 3.617 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\014)]TJ/F126 9.9626 Tf 5.298 -3.617 Td [(/)]TJ/F123 7.5716 Tf 3.717 3.617 Td [(n)]TJ ET q 1 0 0 1 243.676 534.534 cm []0 d 0 J 0.458 w 0 0 m 36.611 0 l S Q BT /F123 9.9626 Tf 257.887 524.97 Td [(n)]TJ/F121 9.9626 Tf 5.43 0 Td [(W)]TJ/F126 9.9626 Tf 18.166 7.074 Td [(;)]TJ/F117 9.9626 Tf 14.92 0 Td [(for)]TJ/F123 9.9626 Tf 14.376 0 Td [(x)]TJ/F126 9.9626 Tf 8.078 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(:)]TJ/F117 9.9626 Tf 63.917 0 Td 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cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -503.256 cm BT /F117 9.9626 Tf 39.797 491.301 Td [(Hence,)]TJ/F123 9.9626 Tf 31.133 0 Td [(I)]TJ/F126 9.9626 Tf 4.902 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.616 Td [(/)]TJ/F117 9.9626 Tf 6.207 0 Td [(satis\002es)-250(that)]TJ ET 1 0 0 1 39.797 491.301 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -491.301 cm BT /F123 9.9626 Tf 64.395 470.478 Td [(E)]TJ/F151 9.9626 Tf 8.644 10.999 Td [(\020)]TJ/F117 9.9626 Tf 5.429 -10.999 Td [(e)15(xp)]TJ/F151 9.9626 Tf 15.897 10.999 Td [(n)]TJ/F121 9.9626 Tf 5.44 -10.999 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\025)]TJ/F123 9.9626 Tf 6.157 0 Td [(I)]TJ/F126 9.9626 Tf 4.901 0 Td [(.\030)]TJ/F121 7.5716 Tf 9.056 4.115 Td [(")]TJ/F126 7.5716 Tf 4.665 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -4.115 Td [(/)]TJ/F151 9.9626 Tf 3.716 10.999 Td [(o\021)]TJ/F121 9.9626 Tf 13.636 -10.999 Td [(D)]TJ/F117 9.9626 Tf 10.538 0 Td [(e)]TJ/F121 7.5716 Tf 4.424 4.115 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(.\025)-15(=)]TJ/F123 7.5716 Tf 10.638 0 Td [(c)]TJ/F126 7.5716 Tf 3.513 0 Td [(/)]TJ/F117 5.9776 Tf 2.824 2.748 Td [(1)]TJ/F126 5.9776 Tf 2.989 0 Td [(=\013)]TJ/F126 9.9626 Tf 7.458 -6.863 Td [(;)-1167(\025)]TJ/F121 9.9626 Tf 23.138 0 Td [(\025)]TJ/F117 9.9626 Tf 10.279 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ ET 1 0 0 1 39.797 470.478 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -470.478 cm BT /F117 9.9626 Tf 39.797 447.854 Td [(and)-250(its)-250(density)]TJ/F123 9.9626 Tf 61.2 0 Td [(p)]TJ/F121 7.5716 Tf 5.29 3.616 Td [(")]TJ/F126 7.5716 Tf 4.664 0 Td [(;)]TJ/F117 7.5716 Tf 2.506 0 Td [(n)]TJ/F126 9.9626 Tf 4.284 -3.616 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F117 9.9626 Tf 6.207 0 Td [(is)-250(gi)25(v)15(en)-250(by)]TJ/F126 9.9626 Tf 45.818 0 Td [(\032)]TJ/F123 7.5716 Tf 5.429 -2.599 Td [(c)]TJ/F117 5.9776 Tf 3.514 2.188 Td [(1)]TJ/F126 5.9776 Tf 2.988 0 Td [(=\013)]TJ/F126 9.9626 Tf 7.458 0.411 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(=\013)-40(/)]TJ/F117 9.9626 Tf 14.485 0 Td [(,)-250(which)-250(pro)15(v)15(es)-250(the)-250(\002rst)-250(part)-250(of)-250(the)-250(theorem.)]TJ ET 1 0 0 1 39.797 447.854 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -447.854 cm BT /F117 9.9626 Tf 51.752 433.705 Td [(Finally)-250(from)]TJ ET 1 0 0 1 104.334 433.705 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -104.334 -433.705 cm BT /F117 9.9626 Tf 104.334 433.705 Td [(\0505.14\051)]TJ ET 1 0 0 1 128.404 433.705 cm 0 g 0 G 1 0 0 1 -128.404 -433.705 cm BT /F117 9.9626 Tf 128.404 433.705 Td [(,)-250(we)-250(deduce)-250(that)-250(the)-250(density)-250(of)]TJ/F123 9.9626 Tf 124.721 0 Td [(X)]TJ/F126 7.5716 Tf 7.103 4.984 Td [(.)]TJ/F117 7.5716 Tf 2.825 0 Td [(0)]TJ/F126 7.5716 Tf 3.785 0 Td [(/)]TJ/F117 7.5716 Tf -6.909 -8.314 Td [(1)]TJ/F117 9.9626 Tf 12.722 3.33 Td [(is)-250(gi)25(v)15(en)-250(by)]TJ ET 1 0 0 1 39.797 433.705 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -433.705 cm BT /F123 9.9626 Tf 64.853 406.682 Td [(p)]TJ/F117 7.5716 Tf 4.991 -1.498 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.498 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)-278(\000)]TJ/F123 9.9626 Tf 22.519 6.984 Td [(c)]TJ/F121 7.5716 Tf 4.622 3.616 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ ET q 1 0 0 1 109.411 409.173 cm []0 d 0 J 0.458 w 0 0 m 20.842 0 l S Q BT /F126 9.9626 Tf 109.411 399.608 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(m)]TJ/F126 9.9626 Tf 7.781 0 Td [(\031)]TJ/F121 7.5716 Tf 13.013 18.642 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.104 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.882 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F40 9.9626 Tf 5.585 11.418 Td [(\000)]TJ/F151 9.9626 Tf 9.235 10.999 Td [(\020)]TJ/F117 9.9626 Tf 5.43 -10.999 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F123 9.9626 Tf 11.509 6.984 Td [(n)]TJ ET q 1 0 0 1 181.906 409.173 cm []0 d 0 J 0.458 w 0 0 m 6.087 0 l S Q BT /F126 9.9626 Tf 181.906 399.608 Td [(\013)]TJ/F151 9.9626 Tf 7.283 18.073 Td [(\021)]TJ/F117 9.9626 Tf 7.09 -10.999 Td [(sin)]TJ/F151 9.9626 Tf 13.286 10.999 Td [(\020)]TJ/F126 9.9626 Tf 6.626 -4.015 Td [(\031)]TJ/F123 9.9626 Tf 6.973 0 Td [(n)]TJ ET q 1 0 0 1 216.191 409.173 cm []0 d 0 J 0.458 w 0 0 m 12.403 0 l S Q BT /F126 9.9626 Tf 219.349 399.608 Td [(\013)]TJ/F151 9.9626 Tf 10.441 18.073 Td [(\021)]TJ/F126 9.9626 Tf 8.285 -4.015 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 8.04 0 Td [(x)]TJ/F117 7.5716 Tf 5.31 3.616 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F126 9.9626 Tf 8.683 -3.616 Td [(/)]TJ/F123 7.5716 Tf 3.716 3.616 Td [(n)]TJ ET q 1 0 0 1 238.075 409.173 cm []0 d 0 J 0.458 w 0 0 m 37.876 0 l S Q BT /F123 9.9626 Tf 252.918 399.608 Td [(n)]TJ/F121 9.9626 Tf 5.43 0 Td [(W)]TJ/F126 9.9626 Tf 18.798 7.074 Td [(;)]TJ/F117 9.9626 Tf 14.921 0 Td [(for)]TJ/F123 9.9626 Tf 14.376 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.982 0 Td [(:)]TJ ET 1 0 0 1 39.797 406.682 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -406.682 cm BT /F117 9.9626 Tf 39.797 379.766 Td [(The)-250(proof)-250(is)-250(no)25(w)-250(complete.)]TJ/F116 9.9626 Tf 122.051 0 Td [(\004)]TJ ET 1 0 0 1 39.797 379.766 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -22.59 cm 0 g 0 G 1 0 0 1 -35.812 -357.176 cm BT /F124 9.9626 Tf 39.797 357.176 Td [(Theor)18(em)-250(8.)]TJ ET 1 0 0 1 88.315 357.176 cm 0 g 0 G 1 0 0 1 -88.315 -357.176 cm BT /F123 9.9626 Tf 92.3 357.176 Td [(The)-356(e)20(xponential)-356(functional)-429(I)]TJ/F126 9.9626 Tf 117.905 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.77 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(/)]TJ/F121 9.9626 Tf 8.444 0 Td [(D)]TJ/F151 9.9626 Tf 12.499 8.025 Td [(R)]TJ/F121 7.5716 Tf 6.496 -2.923 Td [(1)]TJ/F117 7.5716 Tf -1.933 -8.524 Td [(0)]TJ/F117 9.9626 Tf 11.822 3.422 Td [(e)15(xp)]TJ/F121 9.9626 Tf 14.237 0 Td [(f)]TJ/F126 9.9626 Tf 3.686 0 Td [(\013)-40(\030)]TJ/F121 7.5716 Tf 11.427 3.616 Td [(\003)]TJ/F123 7.5716 Tf -1.096 -6.296 Td [(s)]TJ/F121 9.9626 Tf 5.539 2.68 Td [(g)]TJ/F117 9.9626 Tf 5.346 0 Td [(d)]TJ/F123 9.9626 Tf 4.982 0 Td [(s)-416(has)-357(a)-356(continuous)-356(density)]TJ ET 1 0 0 1 39.797 357.176 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -357.176 cm BT /F123 9.9626 Tf 40.943 345.221 Td [(p)]TJ/F121 7.5716 Tf 5.29 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\001)]TJ/F126 9.9626 Tf 2.769 0 Td [(/)]TJ/F123 9.9626 Tf 7.253 0 Td [(with)-355(r)37(espect)-355(to)-355(the)-355(Lebesgue)-355(measur)37(e)-355(whic)15(h)-355(has)-355(the)-355(following)-355(r)37(epr)37(esentation)-355(by)-355(power)]TJ ET 1 0 0 1 39.797 345.221 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -345.221 cm BT /F123 9.9626 Tf 39.797 333.265 Td [(series)]TJ ET 1 0 0 1 39.797 333.265 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -333.265 cm BT /F123 9.9626 Tf 64.853 309.428 Td [(p)]TJ/F121 7.5716 Tf 5.29 4.115 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 10.539 0 Td [(c)]TJ/F117 7.5716 Tf 4.622 4.115 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F121 7.5716 Tf 13.527 7.453 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.103 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.883 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.905 0 Td [(1)]TJ/F126 9.9626 Tf 42.363 18.402 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(n)]TJ/F121 9.9626 Tf 7.644 0 Td [(\000)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ ET q 1 0 0 1 136.608 311.919 cm []0 d 0 J 0.458 w 0 0 m 99.86 0 l S Q BT /F40 9.9626 Tf 136.608 302.355 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)]TJ/F123 9.9626 Tf 9.803 0 Td [(n)]TJ/F126 9.9626 Tf 5.43 0 Td [(/)]TJ/F40 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 7.771 0 Td [(n)]TJ/F121 9.9626 Tf 7.644 0 Td [(C)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(=\013)-40(/)]TJ/F123 9.9626 Tf 15.951 7.073 Td [(x)]TJ/F126 7.5716 Tf 5.31 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.45 0 Td [(2)]TJ/F121 7.5716 Tf 3.786 0 Td [(\000)]TJ/F123 7.5716 Tf 5.906 0 Td [(n)]TJ/F126 7.5716 Tf 4.126 0 Td [(\013)-40(/)]TJ/F126 9.9626 Tf 7.949 -4.115 Td [(;)]TJ/F123 9.9626 Tf 14.921 0 Td [(for)-300(x)]TJ/F126 9.9626 Tf 22.692 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ ET 1 0 0 1 39.797 309.428 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -309.428 cm BT /F123 9.9626 Tf 39.797 280.527 Td [(wher)37(e)-250(c)]TJ/F121 9.9626 Tf 33.86 0 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(c)]TJ/F121 7.5716 Tf 4.424 -1.495 Td [(C)]TJ/F40 9.9626 Tf 6.404 1.495 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(2)]TJ/F121 9.9626 Tf 7.195 0 Td [(\000)]TJ/F126 9.9626 Tf 9.985 0 Td [(\013)-40(/\013)]TJ/F121 7.5716 Tf 15.89 3.616 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 4.284 -3.616 Td [(.\013)]TJ/F121 9.9626 Tf 12.017 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(/)]TJ/F121 7.5716 Tf 3.716 3.616 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 7.051 -3.616 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(:)]TJ ET 1 0 0 1 39.797 280.527 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -19.438 cm 0 g 0 G 1 0 0 1 -35.812 -261.089 cm BT /F124 9.9626 Tf 39.797 261.089 Td [(Pr)18(oof)15(.)]TJ ET 1 0 0 1 65.75 261.089 cm 0 g 0 G 1 0 0 1 -65.75 -261.089 cm BT /F117 9.9626 Tf 69.735 261.089 Td [(First,)-318(let)-318(us)-318(de\002ne)]TJ/F121 9.9626 Tf 79.383 2.092 Td [(O)]TJ/F123 9.9626 Tf -2.007 -2.092 Td [(X)]TJ/F121 9.9626 Tf 11.128 0 Td [(D)-404(\000)]TJ/F123 9.9626 Tf 20.334 0 Td [(X)]TJ/F117 9.9626 Tf 10.273 0 Td [(and)-318(denote)-318(by)]TJ/F121 9.9626 Tf 61.803 2.117 Td [(O)]TJ/F124 9.9626 Tf -1.385 -2.117 Td [(P)]TJ/F117 9.9626 Tf 9.257 0 Td [(for)-318(its)-318(la)15(w)-318(starting)-319(from)-318(0.)-318(Note)-318(that)-319(the)]TJ ET 1 0 0 1 39.797 261.089 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -261.089 cm BT /F117 9.9626 Tf 39.797 249.134 Td [(process)]TJ/F126 9.9626 Tf 33.586 0 Td [(.)]TJ/F123 9.9626 Tf 4.483 0 Td [(X)]TJ/F126 9.9626 Tf 6.754 0 Td [(;)]TJ/F121 9.9626 Tf 6.343 2.117 Td [(O)]TJ/F124 9.9626 Tf -1.385 -2.117 Td [(P)]TJ/F126 9.9626 Tf 6.088 0 Td [(/)]TJ/F117 9.9626 Tf 7.424 0 Td [(is)-372(a)-372(stable)-373(L)]TJ 52.075 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-372(process)-372(with)-373(no)-372(ne)15(g)5(ati)25(v)15(e)-372(jumps)-372(of)-372(inde)15(x)]TJ/F126 9.9626 Tf 189.405 0 Td [(\013)]TJ/F121 9.9626 Tf 11.109 0 Td [(2)]TJ/F126 9.9626 Tf 11.288 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(2)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F117 9.9626 Tf 7.424 0 Td [(starting)]TJ ET 1 0 0 1 39.797 249.134 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -249.134 cm BT /F117 9.9626 Tf 39.797 237.179 Td [(from)-265(0.)-265(From)-266(the)-265(Lamperti)-265(representation,)-265(it)-265(is)-265(clear)-266(that)]TJ/F123 9.9626 Tf 229.187 0 Td [(T)]TJ/F121 9.9626 Tf 10.091 0 Td [(D)]TJ/F123 9.9626 Tf 11.526 0 Td [(I)]TJ/F126 9.9626 Tf 4.901 0 Td [(.)]TJ/F121 9.9626 Tf 3.717 0 Td [(\000)]TJ/F126 9.9626 Tf 7.77 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(/)]TJ/F117 9.9626 Tf 6.358 0 Td [(and)-265(from)-265(the)-266(self-simi)1(lar)]TJ ET 1 0 0 1 39.797 237.179 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -237.179 cm BT /F117 9.9626 Tf 39.797 225.224 Td [(property)65(,)-250(we)-250(ha)20(v)15(e)]TJ ET 1 0 0 1 39.797 225.224 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -225.224 cm BT /F124 9.9626 Tf 63.707 201.139 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.498 Td [(.)]TJ/F123 9.9626 Tf 3.945 0 Td [(T)]TJ/F126 9.9626 Tf 9.811 0 Td [(>)]TJ/F123 9.9626 Tf 10.539 0 Td [(t)]TJ/F126 9.9626 Tf 3.666 0 Td [(/)]TJ/F121 9.9626 Tf 7.203 0 Td [(D)]TJ/F124 9.9626 Tf 11.258 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(0)]TJ/F126 9.9626 Tf 4.284 1.498 Td [(.\033)]TJ/F121 7.5716 Tf 10.331 4.294 Td [(\000)]TJ -1.295 -7.625 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 7.051 3.331 Td [(>)]TJ/F123 9.9626 Tf 10.538 0 Td [(t)]TJ/F126 9.9626 Tf 3.666 0 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)]TJ/F124 9.9626 Tf 10.538 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(0)]TJ/F151 9.9626 Tf 5.944 15.485 Td [(\022)]TJ/F117 9.9626 Tf 11.886 -13.987 Td [(inf)]TJ/F117 7.5716 Tf -5.161 -6.935 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(t)]TJ/F123 9.9626 Tf 5.213 6.935 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.495 Td [(s)]TJ/F126 9.9626 Tf 6.665 1.495 Td [(>)]TJ/F121 9.9626 Tf 10.538 0 Td [(\000)]TJ/F117 9.9626 Tf 7.771 0 Td [(1)]TJ/F151 9.9626 Tf 4.981 13.987 Td [(\023)]TJ ET 1 0 0 1 39.797 201.139 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -201.139 cm BT /F121 9.9626 Tf 109.242 170.255 Td [(D)]TJ/F124 9.9626 Tf 11.258 0 Td [(P)]TJ/F117 7.5716 Tf 6.087 -1.498 Td [(0)]TJ/F151 9.9626 Tf 5.944 15.485 Td [(\022)]TJ/F123 9.9626 Tf 6.725 -13.987 Td [(t)]TJ/F117 7.5716 Tf 3.666 4.114 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F117 9.9626 Tf 16.004 -4.114 Td [(inf)]TJ/F117 7.5716 Tf -5.661 -6.935 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F117 7.5716 Tf 5.709 0 Td [(1)]TJ/F123 9.9626 Tf 6.213 6.935 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.495 Td [(s)]TJ/F126 9.9626 Tf 6.665 1.495 Td [(>)]TJ/F121 9.9626 Tf 10.538 0 Td [(\000)]TJ/F117 9.9626 Tf 7.771 0 Td [(1)]TJ/F151 9.9626 Tf 4.981 13.987 Td [(\023)]TJ/F121 9.9626 Tf 9.492 -13.987 Td [(D)]TJ 11.923 2.117 Td [(O)]TJ/F124 9.9626 Tf -1.385 -2.117 Td [(P)]TJ/F151 9.9626 Tf 7.748 16.976 Td [(\040)]TJ/F123 9.9626 Tf 6.904 -16.976 Td [(t)]TJ/F117 7.5716 Tf 3.666 4.114 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F117 9.9626 Tf 14.619 -4.114 Td [(sup)]TJ/F117 7.5716 Tf -4.276 -9.092 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F117 7.5716 Tf 5.709 0 Td [(1)]TJ/F123 9.9626 Tf 6.213 9.092 Td [(X)]TJ/F123 7.5716 Tf 6.805 -1.495 Td [(s)]TJ/F126 9.9626 Tf 6.665 1.495 Td [(<)]TJ/F117 9.9626 Tf 10.538 0 Td [(1)]TJ/F151 9.9626 Tf 4.981 16.976 Td [(!)]TJ ET 1 0 0 1 39.797 170.255 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -170.255 cm BT /F121 9.9626 Tf 109.242 129.995 Td [(D)]TJ 12.642 2.117 Td [(O)]TJ/F124 9.9626 Tf -1.384 -2.117 Td [(P)]TJ/F151 9.9626 Tf 7.747 22.954 Td [(0)]TJ 0 -17.474 Td [(B)]TJ 0 -6.436 Td [(@)]TJ 7.96 23.91 Td [(0)]TJ 0 -17.474 Td [(B)]TJ 0 -6.436 Td [(@)]TJ/F117 9.9626 Tf 24.425 7.94 Td [(1)]TJ ET q 1 0 0 1 145.363 132.486 cm []0 d 0 J 0.458 w 0 0 m 35.519 0 l S Q BT /F117 9.9626 Tf 149.639 122.922 Td [(sup)]TJ/F117 7.5716 Tf -4.276 -9.092 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.399 0 Td [(\024)]TJ/F117 7.5716 Tf 5.709 0 Td [(1)]TJ/F123 9.9626 Tf 6.214 9.092 Td [(X)]TJ/F123 7.5716 Tf 6.804 -1.495 Td [(s)]TJ/F151 9.9626 Tf 5.093 31.522 Td [(1)]TJ 0 -17.474 Td [(C)]TJ 0 -6.436 Td [(A)]TJ/F126 7.5716 Tf 7.961 21.446 Td [(\013)]TJ/F126 9.9626 Tf 7.891 -20.49 Td [(>)]TJ/F123 9.9626 Tf 10.538 0 Td [(t)]TJ/F151 9.9626 Tf 3.667 22.954 Td [(1)]TJ 0 -17.474 Td [(C)]TJ 0 -6.436 Td [(A)]TJ/F126 9.9626 Tf 9.62 0.956 Td [(:)]TJ ET 1 0 0 1 39.797 129.995 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -129.995 cm BT /F117 9.9626 Tf 39.797 96.059 Td [(Hence)-210(the)-211(e)15(xponential)-210(functional)]TJ/F123 9.9626 Tf 133.441 0 Td [(I)]TJ/F126 9.9626 Tf 4.901 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.771 0 Td [(\030)]TJ/F121 7.5716 Tf 5.34 3.616 Td [(\003)]TJ/F126 9.9626 Tf 4.443 -3.616 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(,)-210(under)]TJ/F124 9.9626 Tf 29.366 0 Td [(P)]TJ/F117 7.5716 Tf 6.088 -1.498 Td [(1)]TJ/F117 9.9626 Tf 4.284 1.498 Td [(,)-210(has)-211(the)-210(same)-210(la)15(w)-211(a)1(s)]TJ/F126 9.9626 Tf 83.524 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(sup)]TJ/F117 7.5716 Tf 13.838 -2.536 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F117 7.5716 Tf 5.709 0 Td [(1)]TJ/F123 9.9626 Tf 6.711 2.536 Td [(X)]TJ/F117 7.5716 Tf 6.805 -1.498 Td [(1)]TJ/F126 9.9626 Tf 4.284 1.498 Td [(/)]TJ/F121 7.5716 Tf 3.716 3.616 Td [(\000)]TJ/F126 7.5716 Tf 5.906 0 Td [(\013)]TJ/F117 9.9626 Tf 5.124 -3.616 Td [(,)-210(under)]TJ ET 1 0 0 1 39.797 96.059 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -96.059 cm BT /F121 9.9626 Tf 41.182 84.05 Td [(O)]TJ/F124 9.9626 Tf -1.385 -2.116 Td [(P)]TJ/F117 9.9626 Tf 6.087 0 Td [(.)]TJ ET 1 0 0 1 39.797 81.934 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -81.934 cm BT /F117 9.9626 Tf 51.752 69.724 Td [(Recently)65(,)-310(Bern)15(yk,)-310(Dalang)-310(and)-310(Peskir)-311([)]TJ ET 1 0 0 1 207.512 69.724 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -207.512 -69.724 cm BT /F117 9.9626 Tf 207.512 69.724 Td [(1)]TJ ET 1 0 0 1 212.494 69.724 cm 0 g 0 G 1 0 0 1 -212.494 -69.724 cm BT /F117 9.9626 Tf 212.494 69.724 Td [(])-310(computed)-310(the)-310(density)-310(of)-310(the)-310(supremum)-310(of)-311(a)-310(stable)]TJ ET 1 0 0 1 39.797 69.724 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -69.724 cm BT /F117 9.9626 Tf 39.797 57.769 Td [(L)]TJ 6.64 0.05 Td [(\264)]TJ -0.553 -0.05 Td [(evy)-269(process)-268(with)-269(no)-268(ne)15(g)5(ati)25(v)15(e)-269(jumps)-268(of)-269(inde)15(x)]TJ/F126 9.9626 Tf 181.146 0 Td [(\013)]TJ/F121 9.9626 Tf 9.197 0 Td [(2)]TJ/F126 9.9626 Tf 9.377 0 Td [(.)]TJ/F117 9.9626 Tf 3.716 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ/F117 9.9626 Tf 4.958 0 Td [(2)]TJ/F126 9.9626 Tf 4.982 0 Td [(/)]TJ/F117 9.9626 Tf 3.716 0 Td [(.)-269(More)-268(precisely)-269(with)-268(our)-269(notation,)-269(t)1(he)]TJ ET 1 0 0 1 39.797 57.769 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -11.955 cm 0 g 0 G 1 0 0 1 382.565 0 cm 0 g 0 G endstream endobj 149 0 obj <> endobj 150 0 obj <> /ProcSet [ /PDF /Text ] >> endobj 151 0 obj <>stream 1 0 0 1 45.354 629.624 cm 0 g 0 G 1 0 0 1 -45.354 -629.624 cm BT /F123 7.9701 Tf 92.53 629.624 Td [(L.)-250(Chaumont)-250(et)-250(al.)-250(/)-250(Stoc)15(hastic)-250(Pr)45(ocesses)-250(and)-250(their)-250(Applications)-250(119)-250(\0502009\051)-250(980\2261000)]TJ/F117 7.9701 Tf 323.435 0 Td [(999)]TJ ET 1 0 0 1 427.92 629.624 cm 0 g 0 G 1 0 0 1 -427.92 -629.624 cm BT /F117 9.9626 Tf 45.354 607.707 Td [(density)]TJ/F123 9.9626 Tf 33.455 0 Td [(f)]TJ/F117 9.9626 Tf 7.342 0 Td [(of)-250(sup)]TJ/F117 7.5716 Tf 24.627 -2.536 Td [(0)]TJ/F121 7.5716 Tf 3.786 0 Td [(\024)]TJ/F123 7.5716 Tf 5.709 0 Td [(s)]TJ/F121 7.5716 Tf 3.4 0 Td [(\024)]TJ/F117 7.5716 Tf 5.709 0 Td [(1)]TJ/F123 9.9626 Tf 6.711 2.536 Td [(X)]TJ/F117 7.5716 Tf 6.805 -1.498 Td [(1)]TJ/F117 9.9626 Tf 4.284 1.498 Td [(,)-250(under)]TJ/F121 9.9626 Tf 31.541 2.117 Td [(O)]TJ/F124 9.9626 Tf -1.384 -2.117 Td [(P)]TJ/F117 9.9626 Tf 6.087 0 Td [(,)-250(is)-250(described)-250(as)-250(follo)25(ws)]TJ ET 1 0 0 1 45.354 607.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -607.707 cm BT /F123 9.9626 Tf 71.446 581.015 Td [(f)]TJ/F126 9.9626 Tf 4.852 0 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.31 0 Td [(/)]TJ/F121 9.9626 Tf 6.484 0 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(c)]TJ/F117 7.5716 Tf 4.623 4.114 Td [(1)]TJ/F126 7.5716 Tf 3.785 0 Td [(=\013)]TJ/F121 7.5716 Tf 13.527 7.454 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.104 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.882 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 42.362 18.402 Td [(\013)]TJ/F123 9.9626 Tf 6.087 0 Td [(n)]TJ/F121 9.9626 Tf 7.644 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ ET q 1 0 0 1 138.32 583.506 cm []0 d 0 J 0.458 w 0 0 m 99.86 0 l S Q BT /F40 9.9626 Tf 138.32 573.941 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)]TJ/F123 9.9626 Tf 9.803 0 Td [(n)]TJ/F126 9.9626 Tf 5.43 0 Td [(/)]TJ/F40 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 7.771 0 Td [(n)]TJ/F121 9.9626 Tf 7.644 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F117 9.9626 Tf 9.984 0 Td [(1)]TJ/F126 9.9626 Tf 4.982 0 Td [(=\013)-40(/)]TJ/F123 9.9626 Tf 15.95 7.074 Td [(x)]TJ/F123 7.5716 Tf 5.31 4.114 Td [(n)]TJ/F126 7.5716 Tf 4.127 0 Td [(\013)]TJ/F121 7.5716 Tf 4.626 0 Td [(\000)]TJ/F117 7.5716 Tf 5.906 0 Td [(2)]TJ/F126 9.9626 Tf 4.284 -4.114 Td [(;)]TJ/F117 9.9626 Tf 14.92 0 Td [(for)]TJ/F123 9.9626 Tf 14.376 0 Td [(x)]TJ/F126 9.9626 Tf 8.078 0 Td [(>)]TJ/F117 9.9626 Tf 10.538 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(:)]TJ ET 1 0 0 1 45.354 581.015 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -581.015 cm BT /F117 9.9626 Tf 45.354 554.293 Td [(Therefore)-250(the)-250(density)]TJ/F123 9.9626 Tf 88.846 0 Td [(p)]TJ/F121 7.5716 Tf 5.29 3.616 Td [(\003)]TJ/F117 9.9626 Tf 6.934 -3.616 Td [(of)]TJ/F123 9.9626 Tf 11.497 0 Td [(I)]TJ/F121 7.5716 Tf 4.623 3.616 Td [(\003)]TJ/F117 9.9626 Tf 6.933 -3.616 Td [(is)-250(gi)25(v)15(en)-250(by)]TJ ET 1 0 0 1 45.354 554.293 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -554.293 cm BT /F123 9.9626 Tf 70.41 528.994 Td [(p)]TJ/F121 7.5716 Tf 5.291 4.115 Td [(\003)]TJ/F126 9.9626 Tf 4.442 -4.115 Td [(.)]TJ/F123 9.9626 Tf 3.985 0 Td [(x)]TJ/F126 9.9626 Tf 5.311 0 Td [(/)]TJ/F121 9.9626 Tf 6.483 0 Td [(D)]TJ/F123 9.9626 Tf 10.538 0 Td [(c)]TJ/F117 7.5716 Tf 4.623 4.115 Td [(1)]TJ/F126 7.5716 Tf 3.786 0 Td [(=\013)]TJ/F121 7.5716 Tf 13.526 7.453 Td [(1)]TJ/F151 9.9626 Tf -3.183 -2.103 Td [(X)]TJ/F123 7.5716 Tf 0.139 -20.883 Td [(n)]TJ/F121 7.5716 Tf 4.127 0 Td [(D)]TJ/F117 7.5716 Tf 5.906 0 Td [(1)]TJ/F126 9.9626 Tf 42.362 18.402 Td [(\013)]TJ/F123 9.9626 Tf 6.088 0 Td [(n)]TJ/F121 9.9626 Tf 7.643 0 Td [(\000)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ ET q 1 0 0 1 142.165 531.485 cm []0 d 0 J 0.458 w 0 0 m 99.86 0 l S Q BT /F40 9.9626 Tf 142.165 521.921 Td [(\000)]TJ/F126 9.9626 Tf 7.574 0 Td [(.\013)]TJ/F123 9.9626 Tf 9.804 0 Td [(n)]TJ/F126 9.9626 Tf 5.429 0 Td [(/)]TJ/F40 9.9626 Tf 3.716 0 Td [(\000)]TJ/F126 9.9626 Tf 7.575 0 Td [(.)]TJ/F121 9.9626 Tf 3.716 0 Td [(\000)]TJ/F123 9.9626 Tf 7.77 0 Td [(n)]TJ/F121 9.9626 Tf 7.644 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F121 9.9626 Tf 7.195 0 Td [(C)]TJ/F117 9.9626 Tf 9.985 0 Td [(1)]TJ/F126 9.9626 Tf 4.981 0 Td [(=\013)-40(/)]TJ/F123 9.9626 Tf 15.95 7.073 Td [(x)]TJ/F126 7.5716 Tf 5.31 4.115 Td [(\013)-40(.)]TJ/F117 7.5716 Tf 7.451 0 Td [(2)]TJ/F121 7.5716 Tf 3.785 0 Td [(\000)]TJ/F123 7.5716 Tf 5.906 0 Td [(n)]TJ/F126 7.5716 Tf 4.127 0 Td [(\013)-40(/)]TJ/F126 9.9626 Tf 7.948 -4.115 Td [(;)]TJ/F117 9.9626 Tf 14.921 0 Td [(for)]TJ/F123 9.9626 Tf 14.376 0 Td [(x)]TJ/F126 9.9626 Tf 8.077 0 Td [(>)]TJ/F117 9.9626 Tf 10.539 0 Td [(0)]TJ/F126 9.9626 Tf 4.981 0 Td [(;)]TJ ET 1 0 0 1 45.354 528.994 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -528.994 cm BT /F117 9.9626 Tf 45.354 502.63 Td [(which)-250(completes)-250(the)-250(proof.)]TJ/F116 9.9626 Tf 120.916 0 Td [(\004)]TJ ET 1 0 0 1 45.354 502.63 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -502.63 cm BT /F124 9.9626 Tf 45.354 473.798 Td [(Ackno)10(wledgement)]TJ ET 1 0 0 1 45.354 473.798 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -473.798 cm BT /F117 9.9626 Tf 57.31 451.023 Td [(The)-250(research)-250(w)10(as)-250(supported)-250(by)-250(EPSRC)-250(grant)-250(EP/D045460/1.)]TJ ET 1 0 0 1 45.354 451.023 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -451.023 cm BT /F124 9.9626 Tf 45.354 428.083 Td [(Refer)18(ences)]TJ ET 1 0 0 1 45.354 428.083 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -20.75 cm 0 g 0 G 1 0 0 1 -45.354 -407.333 cm BT /F117 7.9701 Tf 49.339 407.333 Td [([1])]TJ ET 1 0 0 1 58.632 407.333 cm 0 g 0 G 1 0 0 1 -58.632 -407.333 cm BT /F117 7.9701 Tf 62.618 407.333 Td [(V)129(.)-223(Bern)15(yk,)-223(R.C.)-223(Dalang,)-223(G.)-223(Peskir)40(,)-223(The)-223(la)15(w)-223(of)-223(the)-223(supremum)-223(of)-223(a)-223(stable)-223(L)]TJ 233.807 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-223(process)-223(with)-223(no)-223(ne)15(g)5(ati)25(v)15(e)-223(jumps,)-223(Ann.)]TJ ET 1 0 0 1 45.354 407.333 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -407.333 cm BT /F117 7.9701 Tf 62.618 397.37 Td [(Probab)40(.)-250(\0502008\051)-250(\050in)-250(press\051.)]TJ ET 1 0 0 1 45.354 397.37 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -387.45 cm BT /F117 7.9701 Tf 49.339 387.45 Td [([2])]TJ ET 1 0 0 1 58.632 387.45 cm 0 g 0 G 1 0 0 1 -58.632 -387.45 cm BT /F117 7.9701 Tf 62.618 387.45 Td [(J.)-250(Bertoin,)-250(L)]TJ 40.292 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-250(Processes,)-250(Cambridge)-250(Uni)25(v)15(ersity)-250(Press,)-250(Cambridge,)-250(1996.)]TJ ET 1 0 0 1 45.354 387.45 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -377.53 cm BT /F117 7.9701 Tf 49.339 377.53 Td [([3])]TJ ET 1 0 0 1 58.632 377.53 cm 0 g 0 G 1 0 0 1 -58.632 -377.53 cm BT /F117 7.9701 Tf 62.618 377.53 Td [(J.)-272(Bertoin,)-272(M.E.)-272(Caballero,)-272(Entrance)-272(from)-272(0+)-272(for)-273(increasing)-272(semi-stable)-272(Mark)10(o)15(v)-272(processes,)-272(Bernoulli)-272(8)-272(\0502\051)-272(\0502002\051)]TJ ET 1 0 0 1 45.354 377.53 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -377.53 cm BT /F117 7.9701 Tf 62.618 367.568 Td [(195\226205.)]TJ ET 1 0 0 1 45.354 367.568 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -357.648 cm BT /F117 7.9701 Tf 49.339 357.648 Td [([4])]TJ ET 1 0 0 1 58.632 357.648 cm 0 g 0 G 1 0 0 1 -58.632 -357.648 cm BT /F117 7.9701 Tf 62.618 357.648 Td [(J.)-437(Bertoin,)-438(M.)-438(Y)110(or,)-437(The)-438(entrance)-437(la)15(ws)-438(of)-437(self-similar)-438(Mark)10(o)15(v)-437(processes)-438(and)-437(e)15(xponential)-438(functionals)-437(of)-438(L)]TJ 354.235 0.039 Td [(\264)]TJ -0.442 -0.039 Td [(evy)]TJ ET 1 0 0 1 45.354 357.648 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -357.648 cm BT /F117 7.9701 Tf 62.618 347.685 Td [(processes,)-250(Potential)-250(Anal.)-250(17)-250(\0504\051)-250(\0502002\051)-250(389\226400.)]TJ ET 1 0 0 1 45.354 347.685 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -337.765 cm BT /F117 7.9701 Tf 49.339 337.765 Td [([5])]TJ ET 1 0 0 1 58.632 337.765 cm 0 g 0 G 1 0 0 1 -58.632 -337.765 cm BT /F117 7.9701 Tf 62.618 337.765 Td [(J.)-308(Bertoin,)-309(M.)-308(Y)110(or,)-309(On)-308(the)-309(entire)-308(moments)-309(of)-308(self-similar)-308(Mark)10(o)15(v)-309(processes)-308(and)-309(e)15(xponential)-308(functionals)-309(of)-308(L)]TJ 354.235 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)]TJ ET 1 0 0 1 45.354 337.765 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -337.765 cm BT /F117 7.9701 Tf 62.618 327.802 Td [(processes,)-250(Ann.)-250(F)15(ac.)-250(Sci.)-250(T)80(oulouse)-250(VI)-250(Ser)55(.)-250(Math.)-250(11)-250(\0501\051)-250(\0502002\051)-250(33\22645.)]TJ ET 1 0 0 1 45.354 327.802 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -317.882 cm BT /F117 7.9701 Tf 49.339 317.882 Td [([6])]TJ ET 1 0 0 1 58.632 317.882 cm 0 g 0 G 1 0 0 1 -58.632 -317.882 cm BT /F117 7.9701 Tf 62.618 317.882 Td [(J.)-250(Bertoin,)-250(M.)-250(Y)110(or,)-250(Exponential)-250(functionals)-250(of)-250(L)]TJ 153.419 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-250(processes,)-250(Probab)40(.)-250(Surv)65(.)-250(2)-250(\0502005\051)-250(191\226212.)]TJ ET 1 0 0 1 45.354 317.882 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.919 cm 0 g 0 G 1 0 0 1 -45.354 -307.963 cm BT /F117 7.9701 Tf 49.339 307.963 Td [([7])]TJ ET 1 0 0 1 58.632 307.963 cm 0 g 0 G 1 0 0 1 -58.632 -307.963 cm BT /F117 7.9701 Tf 62.618 307.963 Td [(R.)-291(Blumenthal,)-291(R.K.)-291(Getoor,)-291(D.B.)-291(Ray,)-291(On)-291(the)-291(distrib)20(ution)-291(of)-291(\002rst)-291(hits)-291(for)-291(the)-291(symmetric)-291(stable)-291(processes,)-291(T)35(rans.)]TJ ET 1 0 0 1 45.354 307.963 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -307.963 cm BT /F117 7.9701 Tf 62.618 298 Td [(Amer)55(.)-250(Math.)-250(Soc.)-250(99)-250(\0501961\051)-250(540\226554.)]TJ ET 1 0 0 1 45.354 298 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -288.08 cm BT /F117 7.9701 Tf 49.339 288.08 Td [([8])]TJ ET 1 0 0 1 58.632 288.08 cm 0 g 0 G 1 0 0 1 -58.632 -288.08 cm BT /F117 7.9701 Tf 62.618 288.08 Td [(S.I.)-298(Bo)10(yarchenk)10(o,)-297(S.Z.)-298(Le)25(v)15(endorskii,)-298(Non-Gaussian)-297(Merton\226Black\226Scholes)-298(Theory,)-298(W)80(orld)-297(Scienti\002c,)-298(Sing)5(apore,)]TJ ET 1 0 0 1 45.354 288.08 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -288.08 cm BT /F117 7.9701 Tf 62.618 278.117 Td [(2002.)]TJ ET 1 0 0 1 45.354 278.117 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -268.197 cm BT /F117 7.9701 Tf 49.339 268.197 Td [([9])]TJ ET 1 0 0 1 58.632 268.197 cm 0 g 0 G 1 0 0 1 -58.632 -268.197 cm BT /F117 7.9701 Tf 62.618 268.197 Td [(M.E.)-219(Caballero,)-219(L.)-218(Chaumont,)-219(W)80(eak)-219(con)40(v)15(er)18(gence)-219(of)-219(positi)25(v)15(e)-218(self-similar)-219(Mark)10(o)15(v)-219(processes)-219(and)-218(o)15(v)15(ershoots)-219(of)-219(L)]TJ 354.235 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)]TJ ET 1 0 0 1 45.354 268.197 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -268.197 cm BT /F117 7.9701 Tf 62.618 258.235 Td [(processes,)-250(Ann.)-250(Probab)40(.)-250(34)-250(\0502006\051)-250(1012\2261034.)]TJ ET 1 0 0 1 45.354 258.235 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -248.315 cm BT /F117 7.9701 Tf 45.354 248.315 Td [([10])]TJ ET 1 0 0 1 58.632 248.315 cm 0 g 0 G 1 0 0 1 -58.632 -248.315 cm BT /F117 7.9701 Tf 62.618 248.315 Td [(M.E.)-220(Caball)1(ero,)-220(L.)-220(Chaumont,)-219(Conditioned)-220(stable)-219(L)]TJ 164.805 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-220(processes)-219(and)-220(the)-219(Lamperti)-220(representation,)-219(J.)-220(Appl.)-220(Probab)40(.)]TJ ET 1 0 0 1 45.354 248.315 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -248.315 cm BT /F117 7.9701 Tf 62.618 238.352 Td [(43)-250(\0502006\051)-250(967\226983.)]TJ ET 1 0 0 1 45.354 238.352 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -228.432 cm BT /F117 7.9701 Tf 45.354 228.432 Td [([11])]TJ ET 1 0 0 1 58.632 228.432 cm 0 g 0 G 1 0 0 1 -58.632 -228.432 cm BT /F117 7.9701 Tf 62.618 228.432 Td [(P)111(.)-240(Carr,)-239(H.)-240(Geman,)-240(D.B.)-240(Madan,)-239(M.)-240(Y)110(or,)-240(The)-240(\002ne)-239(structure)-240(of)-240(asset)-239(returns:)-240(An)-240(empirical)-240(in)40(v)15(estig)5(ation,)-239(J.)-240(Business)]TJ ET 1 0 0 1 45.354 228.432 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -228.432 cm BT /F117 7.9701 Tf 62.618 218.47 Td [(75)-250(\0502002\051)-250(305\226332.)]TJ ET 1 0 0 1 45.354 218.47 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -208.55 cm BT /F117 7.9701 Tf 45.354 208.55 Td [([12])]TJ ET 1 0 0 1 58.632 208.55 cm 0 g 0 G 1 0 0 1 -58.632 -208.55 cm BT /F117 7.9701 Tf 62.618 208.55 Td [(L.)-370(Chaumont,)-370(Conditionings)-370(and)-370(path)-370(decompositions)-369(for)-370(L)]TJ 197.754 0.039 Td [(\264)]TJ -0.443 -0.039 Td [(evy)-370(processes,)-370(Stochastic)-370(Process.)-370(Appl.)-370(64)-370(\0501996\051)]TJ ET 1 0 0 1 45.354 208.55 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -208.55 cm BT /F117 7.9701 Tf 62.618 198.587 Td [(39\22654.)]TJ ET 1 0 0 1 45.354 198.587 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -188.667 cm BT /F117 7.9701 Tf 45.354 188.667 Td [([13])]TJ ET 1 0 0 1 58.632 188.667 cm 0 g 0 G 1 0 0 1 -58.632 -188.667 cm BT /F117 7.9701 Tf 62.618 188.667 Td [(L.)-351(Chaumont,)-351(J.C.)-350(P)15(ardo,)-351(The)-351(lo)25(wer)-351(en)40(v)15(elope)-351(of)-350(positi)25(v)15(e)-351(self-similar)-351(Mark)10(o)15(v)-351(processes,)-351(Electron)-350(J.)-351(Probab)40(.)-351(11)]TJ ET 1 0 0 1 45.354 188.667 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -188.667 cm BT /F117 7.9701 Tf 62.618 178.704 Td [(\0502006\051)-250(1321\2261341.)]TJ ET 1 0 0 1 45.354 178.704 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -168.784 cm BT /F117 7.9701 Tf 45.354 168.784 Td [([14])]TJ ET 1 0 0 1 58.632 168.784 cm 0 g 0 G 1 0 0 1 -58.632 -168.784 cm BT /F117 7.9701 Tf 62.618 168.784 Td [(R.)-250(Cont,)-250(P)111(.)-250(T)80(ank)10(o)15(v,)-250(Financial)-250(Modeling)-250(with)-250(Jump)-250(Processes,)-250(Chapman)-250(and)-250(Hall/CRC,)-250(Boca)-250(Raton,)-250(FL,)-250(2004.)]TJ ET 1 0 0 1 45.354 168.784 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.919 cm 0 g 0 G 1 0 0 1 -45.354 -158.865 cm BT /F117 7.9701 Tf 45.354 158.865 Td [([15])]TJ ET 1 0 0 1 58.632 158.865 cm 0 g 0 G 1 0 0 1 -58.632 -158.865 cm BT /F117 7.9701 Tf 62.618 158.865 Td [(R.A.)-211(Done)15(y,)-212(Fluctuation)-211(theory)-212(for)-211(L)]TJ 117.883 0.039 Td [(\264)]TJ -0.442 -0.039 Td [(evy)-211(processes,)-212(in:)-211(Ecole)-212(d')]TJ 84.43 0.039 Td [(\264)]TJ -0.443 -0.039 Td [(et)]TJ 6.197 0.039 Td [(\264)]TJ -0.442 -0.039 Td [(e)-211(de)-212(Probabilit)]TJ 46.317 0.039 Td [(\264)]TJ -0.443 -0.039 Td [(es)-211(de)-212(Saint-Flour,)-211(in:)-212(Lecture)-211(Notes)]TJ ET 1 0 0 1 45.354 158.865 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -158.865 cm BT /F117 7.9701 Tf 62.618 148.902 Td [(in)-250(Mathematics,)-250(v)20(ol.)-250(1897,)-250(Springer,)-250(2007.)]TJ ET 1 0 0 1 45.354 148.902 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -138.982 cm BT /F117 7.9701 Tf 45.354 138.982 Td [([16])]TJ ET 1 0 0 1 58.632 138.982 cm 0 g 0 G 1 0 0 1 -58.632 -138.982 cm BT /F117 7.9701 Tf 62.618 138.982 Td [(R.A.)-322(Done)15(y,)-321(A.E.)-322(K)25(yprianou,)-322(Ov)15(ershoots)-321(and)-322(undershoots)-322(of)-321(L)]TJ 207.341 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-322(processes,)-321(Ann.)-322(Appl.)-322(Probab)40(.)-321(16)-322(\0501\051)-322(\0502006\051)]TJ ET 1 0 0 1 45.354 138.982 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -138.982 cm BT /F117 7.9701 Tf 62.618 129.019 Td [(91\226106.)]TJ ET 1 0 0 1 45.354 129.019 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 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[(S.G.)-250(K)35(ou,)-250(H.)-250(W)80(ang,)-250(First)-250(passage)-250(times)-250(of)-250(a)-250(jump)-250(dif)25(fusion)-250(process,)-250(Adv)65(.)-250(in)-250(Appl.)-250(Probab)40(.)-250(35)-250(\0502003\051)-250(504\226531.)]TJ ET 1 0 0 1 45.354 99.217 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -89.297 cm BT /F117 7.9701 Tf 45.354 89.297 Td [([19])]TJ ET 1 0 0 1 58.632 89.297 cm 0 g 0 G 1 0 0 1 -58.632 -89.297 cm BT /F117 7.9701 Tf 62.618 89.297 Td [(A.E.)-250(K)25(yprianou,)-250(Introductory)-250(Lectures)-250(of)-250(Fluctuations)-250(of)-250(L)]TJ 189.723 0.04 Td [(\264)]TJ -0.443 -0.04 Td [(evy)-250(Processes)-250(with)-250(Applications,)-250(Springer,)-250(2006.)]TJ ET 1 0 0 1 45.354 89.297 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.92 cm 0 g 0 G 1 0 0 1 -45.354 -79.377 cm BT /F117 7.9701 Tf 45.354 79.377 Td [([20])]TJ ET 1 0 0 1 58.632 79.377 cm 0 g 0 G 1 0 0 1 -58.632 -79.377 cm BT /F117 7.9701 Tf 62.618 79.377 Td 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57.06 597.744 Td [(Poincar)]TJ 24.791 0.04 Td [(\264)]TJ -0.443 -0.04 Td [(e)-250(Probab)40(.)-250(Statist.)-250(40)-250(\0503\051)-250(\0502004\051)-250(299\226308.)]TJ ET 1 0 0 1 39.797 597.744 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -587.781 cm BT /F117 7.9701 Tf 39.797 587.781 Td [([23])]TJ ET 1 0 0 1 53.075 587.781 cm 0 g 0 G 1 0 0 1 -53.075 -587.781 cm BT /F117 7.9701 Tf 57.06 587.781 Td [(D.)-851(Monrad,)-852(M.L.)-852(Silv)15(erstein,)-852(Stable)-851(processes:)-853(Sample)-851(function)-852(gro)25(wth)-851(at)-851(a)-852(local)-851(minimum,)-852(Z.)]TJ ET 1 0 0 1 39.797 587.781 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -587.781 cm BT /F117 7.9701 Tf 57.06 577.819 Td [(W)80(ahrscheinlichk)10(eitstheor)55(.)-250(V)111(erw)10(andte)-250(Geb)40(.)-250(49)-250(\0502\051)-250(\0501979\051)-250(177\226210.)]TJ ET 1 0 0 1 39.797 577.819 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -567.856 cm BT /F117 7.9701 Tf 39.797 567.856 Td [([24])]TJ ET 1 0 0 1 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[(ese)-219(de)-219(doctorat)-219(de)-219(l'uni)25(v)15(ersit)]TJ 91.21 0.04 Td [(\264)]TJ -0.443 -0.04 Td [(e)-219(P)15(aris)]TJ ET 1 0 0 1 39.797 547.931 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -547.931 cm BT /F117 7.9701 Tf 57.06 537.968 Td [(VI,)-250(\0502004\051.)]TJ ET 1 0 0 1 39.797 537.968 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -528.005 cm BT /F117 7.9701 Tf 39.797 528.005 Td [([26])]TJ ET 1 0 0 1 53.075 528.005 cm 0 g 0 G 1 0 0 1 -53.075 -528.005 cm BT /F117 7.9701 Tf 57.06 528.005 Td [(V)129(.)-271(Ri)25(v)15(ero,)-272(Recurrent)-271(e)15(xtensions)-272(of)-271(self-similar)-272(Mark)10(o)15(v)-271(processes)-271(and)-272(Cram)]TJ 242.693 0.04 Td [(\264)]TJ -0.443 -0.04 Td [(er')55(s)-271(condition,)-272(Bernoulli)-271(11)-272(\0503\051)-271(\0502005\051)]TJ ET 1 0 0 1 39.797 528.005 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -528.005 cm BT /F117 7.9701 Tf 57.06 518.043 Td [(471\226509.)]TJ ET 1 0 0 1 39.797 518.043 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -508.08 cm BT /F117 7.9701 Tf 39.797 508.08 Td [([27])]TJ ET 1 0 0 1 53.075 508.08 cm 0 g 0 G 1 0 0 1 -53.075 -508.08 cm BT /F117 7.9701 Tf 57.06 508.08 Td [(B.A.)-337(Rogozin,)-337(The)-336(distrib)20(ution)-337(of)-337(the)-337(\002rst)-336(hit)-337(for)-337(stable)-337(and)-337(asymptot)1(ically)-337(stable)-337(random)-337(w)10(alks)-337(on)-336(an)-337(interv)25(al,)]TJ ET 1 0 0 1 39.797 508.08 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -508.08 cm BT /F117 7.9701 Tf 57.06 498.118 Td [(Theory)-250(Probab)40(.)-250(Appl.)-250(17)-250(\0501972\051)-250(332\226338.)]TJ ET 1 0 0 1 39.797 498.118 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -488.155 cm BT /F117 7.9701 Tf 39.797 488.155 Td [([28])]TJ ET 1 0 0 1 53.075 488.155 cm 0 g 0 G 1 0 0 1 -53.075 -488.155 cm BT /F117 7.9701 Tf 57.06 488.155 Td [(K.I.)-250(Sato,)-250(L)]TJ 37.854 0.04 Td [(\264)]TJ -0.442 -0.04 Td [(evy)-250(Processes)-250(and)-250(In\002nitely)-250(Di)25(visible)-250(Distrib)20(utions,)-250(Cambridge)-250(Uni)25(v)15(ersity)-250(Press,)-250(Cambridge,)-250(1999.)]TJ ET 1 0 0 1 39.797 488.155 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.963 cm 0 g 0 G 1 0 0 1 -39.797 -478.192 cm BT /F117 7.9701 Tf 39.797 478.192 Td [([29])]TJ ET 1 0 0 1 53.075 478.192 cm 0 g 0 G 1 0 0 1 -53.075 -478.192 cm BT /F117 7.9701 Tf 57.06 478.192 Td [(W)92(.)-250(Schoutens,)-250(L)]TJ 52.838 0.04 Td [(\264)]TJ -0.443 -0.04 Td [(evy)-250(Processes)-250(in)-250(Finance.)-250(Pricing)-250(Finance)-250(Deri)25(v)25(ati)25(v)15(es,)-250(W)40(ile)15(y,)-250(Ne)25(w)-250(Y)110(ork,)-250(2003.)]TJ ET 1 0 0 1 39.797 478.192 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -9.962 cm 0 g 0 G 1 0 0 1 -39.797 -468.23 cm BT /F117 7.9701 Tf 39.797 468.23 Td [([30])]TJ ET 1 0 0 1 53.075 468.23 cm 0 g 0 G 1 0 0 1 -53.075 -468.23 cm BT /F117 7.9701 Tf 57.06 468.23 Td [(V)129(.M.)-392(Zolotare)25(v,)-393(One-Dimensional)-392(Stable)-392(Distrib)20(utions,)-393(in:)-392(T)35(ranslations)-393(of)-392(Mathematical)-392(Monographs,)-393(v)20(ol.)-392(65,)]TJ ET 1 0 0 1 39.797 468.23 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -468.23 cm BT /F117 7.9701 Tf 57.06 458.267 Td [(American)-250(Mathematical)-250(Society,)-250(Pro)15(vidence,)-250(RI,)-250(1986.)]TJ ET 1 0 0 1 39.797 458.267 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -412.453 cm 0 g 0 G 1 0 0 1 382.565 0 cm 0 g 0 G endstream endobj 155 0 obj <> endobj 156 0 obj <> endobj 157 0 obj <> endobj 158 0 obj <> endobj 159 0 obj <> endobj 160 0 obj <> endobj 161 0 obj <> endobj 162 0 obj <> endobj 163 0 obj [ 777.8 ] endobj 164 0 obj [ 758.3 ] endobj 165 0 obj [ 722.2 ] endobj 166 0 obj [ 627.2 817.8 766.7 692.2 664.4 743.3 715.6 766.7 715.6 ] endobj 167 0 obj [ 555.6 ] endobj 168 0 obj [ 771.4 527.8 718.7 ] endobj 169 0 obj [ 474 474 262 262 325 533 626 626 545 545 675 675 545 545 612 612 612 612 618 618 429 429 1107 1107 693 693 621 621 674 674 674 674 690 690 554 554 1348 1348 866 866 799 799 729 729 729 729 729 729 792 792 792 792 792 792 792 575 799 799 799 799 346 346 984 1235 458 528 1110 1511 1110 1511 1110 1511 1045 940 458 940 940 940 940 940 1415 1269 528 1227 1227 1227 1227 1227 940 1269 742 1075 1408 742 1075 1408 469 469 558 558 558 558 546 546 ] endobj 170 0 obj [ 666.7 611.1 777.8 777.8 388.9 500 777.8 666.7 944.5 722.2 777.8 611.1 777.8 722.2 ] endobj 171 0 obj <>stream %!PS-AdobeFont-1.0: bbold10 001.001 13 dict begin /FontInfo 16 dict dup begin /version (001.001) readonly def /Notice (Generated from MetaFont bitmap by mftrace 1.0.28, http://www.cs.uu.nl/~hanwen/mftrace/ ) readonly def /FullName (bbold10) readonly def /FamilyName (bbold10) readonly def /Weight (regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /EQLWZD+bbold10 def /FontType 1 def /PaintType 0 def /FontMatrix [0.001000 0 0 0.001000 0 0] readonly def /FontBBox {-47 -37 786 1114} readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put readonly def currentdict end currentfile eexec oc;jtDXL6p,x#gYCݠ>W{ˤ&)عGS]5>T@Z6s%@1=wM2yFs"/_wE(gݓ]|]n r9y(;9~|.!nzJVg7qL}9M#H266Rz`J b̯= /gRa@S(`m^ŻMH=~$[dן벫}~"{U&۝jDxEѯ4g:M9YrJuP2w-Yd˭y/4n~ U,O/:B ` IH?z(%Vl!n"t9_vcU`8i&dQ8Fj/%;&FĢ+UȚ2?pn| _Z\<̛ioqj_!iz QY꭫<brǪk%_1--%ox|At:ƄC:d&Qȿ_NWL~=6>4P@x Ub]>̦*4R r8 #oP endstream endobj 172 0 obj <> endobj 173 0 obj <>stream %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /YQOHQL+CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 68 /D put dup 70 /F put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y=cLIPsF'f> ba ]fv+QAwdO[x"%Sx~{p҈덡|O BÄ/GL3h+Ng03jU1~akDzq=U}.KY碌 ֻ1?C N2MhD{4~=p7Lp.MKDdg)~Ukws\?XaIW< =K</1{w|˾9T /;ϓLR Y;n~qUۻA!,tLQpNxع} -oqa*M3X ċ|wXy,)7fHE%{Jvu&Q F:m! }7c:좑K 1 1e>y5nn~j,H2 '37[`ǚ}ܺO ڄzN]IKWoFuЯ,Tm+?Bq)wSso[T^ >T+N6#ٙU͛Lټmä{5hY401KV=LYsk@V a nozB\I^v 5{ |>1pAHendstream endobj 174 0 obj <> endobj 175 0 obj <>stream %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /JGIBOW+CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 70 /F put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y! [R߻*|]~[C֨a[#ԙ jY!4J"3&ejc\J$2626wIaUIrnFB/Г(Hp%#O.,snݸt%\b9?_\ <+n6 ی k&dE}[+f)eD#d|YBշ]j;i`lʗۡIqTb2 ){K9g$,-E$ЉPyRƮ咻7%PTv N{D/y~Ots$m@xf-\ZLR S\)2ؼ^_Yoik.t@s)BtS55SiS>0@aZ[ԇ!&:facendstream endobj 176 0 obj <> endobj 177 0 obj <>stream %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /WRIBEX+CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 8 /Phi put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# ]LeVߐGoo٥\k 9Mՙ= 0)xf 1kX9H!.vPN 7qjj7!6CɫTw.]ʂԬ/J1]0': fqdU24tԡ?@^g+0[ KTB/UٝFMz7 .U{7K.=UٯI CzY^ rP חLТ{tO[SWnƢpR\oxoome9@+Xו}t'Q#}3^XNTRuaU)W Ը=HcX\>f,`7z62謢%ƾ袚ڎ')ܱԟ\m--Tްޞ(<zI|PAƔc۳. :0^S^ v|@*sx[^6+01>cוe9syN:TnSꢂb*[~[̏|jes=woDȐmɵVѦ@^nd694Hl#C49& ꓄C/Fgp$xcHg,  C}lgAQ,2jZD3_4L}%3]AVn]Ns$j~d__`F]!m9ӧ*R~<"ˋx8_Ͻ/J.jPe{亾zZ"q֙;\bF,q ; xӉ߀5O.e.#}Bz3NO8lkY(5MX?" NP Mh@/`qe+ U#w-c+0]g͘L =nkYWSeC2 ϩbGm-"t}h+\_O!>kz3fu 6mƜ mZ)Q7<"^ŗC}⿼";Y[KYX_&'0endstream endobj 178 0 obj <> endobj 179 0 obj <>stream %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MLYEVU+MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 4 /squaresolid put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\cg$4b Mٲ:Ix`(],k pF:ȁ,DN֠L'Y@u7ˍL hFdRs9 9X|",ѯQ5ā$|cs-ւ?ܰځͫ$P<`]; XPǑ%Ęqj ?޷ SK1Q)m*;;\Y#R pD?v-ľ%}JZ2TxI '|?ȗ2II>6|ڵٴ&68Vj/.'Ű򱫳津<Rbh zYŎVc .ʕ4pIG*#5σdc\f;ܾUЏAL$Bj9Ա\Q9$m&O"b"i>T-:\ɥOWൣ)dEHGxe^M.EX1hrhOSru{|cIqUeV]w284莎[BG(p.!*=^^ ^?j?׬/b(O nkW| s7"kl3Rc1N%%Q:j};&#\lA:7VumTԵ :/Ek?/\ԗh>endstream endobj 180 0 obj <> endobj 181 0 obj <>stream %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /QKRSHW+MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 80 /P put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻjf 2mC+ KVŘ31 xb1݅67Â->[$=3]6mY>/i2v| /Odok YFԝyQjY(_6L(+"#H)_T\ ( ;^͘*Vk&AK]l}EƮB+HQ/ ]$9 {'rȀf{ҁ> endobj 183 0 obj <>stream %!FontType1-1.0: msbm8 1.2/19-Jan-95 %%VMusage: 32482 33913 % T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved. 12 dict begin /FontInfo 13 dict dup begin /version (1.2/19-Jan-95) readonly def /Notice (Copyright \(C\) 1994, 1995, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-C.) readonly def /FullName (msbm8) readonly def /FamilyName (msbm8) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -133 def /UnderlineThickness 20 def /Descender -194 def /Ascender 694 def /CapHeight 683 def /XHeight 431 def end readonly def /FontName /BTWKUQ+msbm8 def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /FontBBox [-59 -474 2478 974] readonly def /StrokeWidth 0 def currentdict end currentfile eexec oc;jtD[1ƅpToZQ?1,:ǰ F" t<+<3]jl6Y(Ȇ}wROv9xI^AőS`fMB#DމڄNO&)hˈG);om'.*\?Csp|PTkk;_$ư{4!͸ !|w]@Њm!3J]{jXxH=z 6|Zfs,L kTu4)icrF]G== MVԳdv 3ʸQGc@-W/ʵcc6T=E1Orm&^XL$Ŏ$SΥf{3Kl A~(ڋjfÉU&\'/:m+q&HgŔQުqT50UdV| @zĝWntYf6nyҹ\$"4yN?ULL w5I?X#i =f,g]υ97z7[ ^˿5AMʾ쫻97Ez./|l2"ʸoHѾ1xeŤ1Tvk[-9~Fn&nI’y0LXmu+$T$AW:b5%K4&vZkdb@`eF8n)|_̷rʐtnu=_*duK=h߿KK=;y(>*N%|'+# ]/΃Sx ±KApO.jéIq]LgD'M!O b o?*FgdGKIq9dWxz¬hjvE%lr~9\~$JU(Fϻ>)45*/W 3endstream endobj 184 0 obj <> endobj 185 0 obj <>stream %!PS-AdobeFont-1.1: MTEX 1.1 %%CreationDate: 1993 Jun 26 10:30:36 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. % MathTime is a trademark of The TeXplorators Corporation 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation. Hinting (c) 1992, 1993 Y&Y, Inc. (508) 371-3286. All Rights Reserved.) readonly def /FullName (MTEX) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /FXWMPA+MTEX def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 110 /braceleftBig put dup 40 /braceleftBigg put dup 8 /braceleftbig put dup 26 /braceleftbigg put dup 111 /bracerightBig put dup 41 /bracerightBigg put dup 9 /bracerightbig put dup 27 /bracerightbigg put dup 90 /integraldisplay put dup 82 /integraltext put dup 16 /parenleftBig put dup 32 /parenleftBigg put dup 18 /parenleftbigg put dup 64 /parenleftbt put dup 66 /parenleftex put dup 48 /parenlefttp put dup 17 /parenrightBig put dup 33 /parenrightBigg put dup 19 /parenrightbigg put dup 65 /parenrightbt put dup 67 /parenrightex put dup 49 /parenrighttp put dup 88 /summationdisplay put dup 12 /vextendsingle put readonly def /FontBBox{-23 -2958 1456 766}readonly def currentdict end currentfile eexec oc;j~EЪ+`U+1;[ihHlgtR@nk{#Y~gJ[. DI~ْ+%hapYz;3NO_O:Vп}KBhIϮԬ";eiwzVcW;I0a1]j"4[{ErGT1QeG0 Vw ߚOҎN'·4b>T(4^mѨnV8Bo8cpWTC 6j'-б^3;ZSi 4LTVC}:)EuF+o1F}NNZ*1aD1U(H`b^;1Mac]&'kM.Lؐ1Sh3\9)Wyϋzoԡ!OWr%\ tA7e:蔧R1-~w1Dj EWNTl%4 {yBvV E=&AcW_}in|{^X&V&F ^ G}O׬FuR4DA蟩z:\0+^'x xLH⌌R`LFP'3|q#eh+AWy{}V#P]/!K4C\G>u+NGWѯ# nٷUgYֱ&lO?/.G~s-ӈPm~$K_+ *Jdv TX0mL:c:/LmLHϠIel"yy!%Ev-L}>f};G_ V'#1n%-љ#7!ٜxi Ӻ>~aD uj ! 0tTy.l'8ᄿBt>BZ脚L ۘ#qe4 +Ax!4hpFmLb'!!;4_l ξ_deMQ@46CamA}^I쩎P5qE+̓&J(|yRG@N R,9' j xէD&,3Î(ԗ&;=Sa=a؈&$ 2fJŞȲЧ)1{wkE*Tqsۓ@-xE6J)I u0ޙq Scr]gxl+1mH)ۤ6 ƴH~rL:ZbguŌÑ\-Knb:#_b$ /0FnLO.R1qS%b0,4|c)\qӪtECn߭u?{Ѕ7B9)8M#;tP\ޑwHpS .*P2D4XAI`M[s+C[h wĠsf>PE_@qȵ bQo' x "Kx#L:O{Ӄ1_yyH+a̦"tJZҨ|C1F5) \-DصdKjSS։8$0v1ڧv|/ށ06hnSل3pxDr⡣5,Y]VD.]uz}j+Q- KݥxL94(2`R}vˈbX|$wq.?侃&"5;SqX +w>r7!1Ngx,!IUvDJ6o })ыu{莝'r.Y9L2aNd#D}"bb5ЪO؃68+`eo>XZv?SnܻO~cI91T He*"¡jHԤDžI\TT Oa:p<Α+;A'g8v:E!D@_" OuNJCr D,ip'YG4z^(ފ$ Z t > ȸOb>~T]ٸ XP7gX8p%T_t=\^n㗗t#Z Z,eauϠ\iiCYdS%eBOgWF$xz;zMzs`鴩xΤ^%r l@ ǿL)Z@ik59ID(ĥQ9RX@EqDςhʛ 3ʞۖ`F b Q}_u5_'jl*J-UzM)j_ޱk*=ie6{ӫb'(O^0p121mc2?n-蕬4.}>v/#7xE"04Jr %uE.̠N 6FCo08BL_Qb PȽsMchrXZ~YuXbP]ܡ6)B<k ƙ)C!~ ev4Tt^'Y^-n+чJ6u%s8=b_=BsppEni:,8#CsxD6iR.+C'䫣d'<&awYo2{FNin&9v BȜ/ G>'R:7kN FYٞvP`,}˄-:щ6br 56Ԕxu=[b!m !x؟k3cNR絋qqbsV4rKP&ARg\3z?9;eJs}[[&;fi4L6`jZsQjՌ8pZa ̔}:fa$]8KIϫfy^zd*Ep׃C{Gn{'*-CK99*ov ƒZb 06 Nma9]W=n?Lc:9',,T 0LxHJ2_5bQy\t%0+ zW6ۄo#xL11&-Z̸]0MIroP[G2/$יkM-a3PR2As8롉|p2&¬G 0oX'L#13~-~(PٞLwksSc)PRY TW^v뭏"bu0O\"bSg~/ZT~^ y򧑈( (5B@goIv4B]6QtՋ)U_ꖟN1|XyCnyVoRdALΠ%^.oiro [`a"'Vq?QgbI*nTqW?m.cAdV >ޓhUHH.8Dlp!]׌*} HPendstream endobj 186 0 obj <> endobj 187 0 obj <> /Width 73 /ColorSpace /DeviceRGB /Height 106 >>stream x\yPSW?$Y I nHk-.j_cvIuNIVigtv[)uHMH`DH $aIbr!~/ ֊ǝ{<ιq1Cf'6;Ǜ@EH'Bnn.Lf2LddӘGMe||i ;^~e/<'WyE n/{/g~'ƿѝq1 ?JR X,"t:j'V5--aŊccc"())I,[LNfV+A*J FkkkAAAuu5`۶m\.w”G+dd2H$&\'4  @8p8,O"޸ Q6d_~9~L$RǦYO4xuf'6;13mHT6bd2LW^E HRT* SE#=B΁rb cUTtFt:ӑ-Yp8TgϞׯHQ˗/GEEQ(Er@@$333׭['VkttD"Yx|_HH^r(jҥX,600y#<ϣ3?>ʘxԩ{%y6SNnh4nwWW8Fh?Kܗ_Ϻ\.`0  `0NNWWW/]^+--5LJrҥ$hL&p֭Abl^d2 ¼t'}цX 57{IT 7wfr\}ӻk,//ONNF'O$t0xbf/M&ߴiÇ?9s0 GFFVVV>3f`#ŋ+Vg'N ~)bf6e6o1 \K<0 0 |>* 4p8x'& Ǘ2"uJ߷l)))v`ްa@ `0\.W"8? 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Hϟ?⼼<ݞRXXf!JRZV"h4GVVVnJeee+++KKKl2<<\XXVZ-L~={1 WD>众;ӌwg4S*3ND8v\'GGGVkBBb #"=AA|>cccbw E=l6f5 :6mڤRNhBB*BP(APh4t<ODv{dddooD"YdIYY^7 ===2p bZBaMM !mmmT*U*.^l6߾}ѣ7nHOOA0""bhh رcϟ?v9{>s Trt:]`` jxT^'3W.jLАne8dX @ |:ݻGFFx|ZZNryyyW\a2ŋ|>D"i4zoA?xUCCCrrrVX1fI`2'_wF$Hdy2p8NJLLZh4zZ3cbb.]zU>p( ;{naa7l60 ۷OBy< <r)'Nrg2t۷o̙(w-2U&=s1єl:uVR`ww7L7nlkk#8NHr֭[wMLhV\ؘJT*\.APTzB ANJJvJOOl;w xV5..*++AAARg*'Nxmtt EkkkrrV5L'OKMMmkks8k4 +{EOӬ3=k~ы߄L>իʸճ&377£ѳݭVd<f۶m/_Z<@ ATfr\.GEEuvvFGGx!bX.FF< )))===D"̝;J&''߻wǺeggϛ7O&TTThAR/_n0i4ɴX,x<>++/Xd2 Be2ٽ{t` ӞskԌ7xyyybMNNxbFq:nիW_/_ѣQ???AvypT[_"mF|1|{ Q `nsC': N07t `nsC': N07t `nsC': N07t `nsC': N07t `no4)endstream endobj 208 0 obj <>stream pdfTeX-1.40.3 application/pdf Some explicit identities associated with positive self-similar Markov processes L. Chaumont; A.E. Kyprianou; J.C. Pardo Positive self-similar Markov processesLamperti representationConditioned stable Lévy processesFirst exit timeFirst hitting timeExponential functional journal Stochastic Processes and their Applications Copyright © 2008 Elsevier B.V. All rights reserved. Elsevier B.V. 0304-4149 119 3 March 2009 Stochastic Processes and their Applications 980-1000 980 1000 10.1016/j.spa.2008.05.001 http://dx.doi.org/10.1016/j.spa.2008.05.001 doi:10.1016/j.spa.2008.05.001 sciencedirect.com elsevier.com 1 B Elsevier True 2009-02-16T11:40:44+05:30 2009-02-16T11:40:44+05:30 2009-02-16T11:40:44+05:30 endstream endobj 209 0 obj <>stream xڝwTTϽwz0z.0. 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