Poisson type approximations for sums of dependent variables ; Priklausomų atsitiktinių dydžių sumų aproksimavimas Puasono tipo matais

Sujets

• Compound Poisson distribution
• Mathematics

Informations

• Publié par: vilnius_university
• Publié le: 01 janvier 2011
• Nombre de lectures: 31

Extrait

PhVILNIAEUSORUNIVERSITYARIABLESJ(01OFuratENT
ctoraleSciences,PVilnius,etrauskienSUMS
DePENDPOISSONVTYPEDoAPPDissertationRysicalOMathematicsXIMAP)TIONS2011F?ekThecscienyticP)w?iusorksicwiasacavrUnivriPhedScieoutMathemaduring-2006-2010ydatsVilananiusiUniv(Vilniuseritersity,Scienyticalsupnervisor:es,Prof.tDr.csHabil01.2VSVILNIAAPRUSP)UNIVERSITETTIPOASmokslai,JSUMUVIMASuratT
disertacijaeaP2011etrauskien
OKSIMAePUASONOPRIKLAMAUSOMUAIDaktaroAFiziniaiTSITIKTINIUmatematik(01DVilnius,YD?IU01Disertacija(Vilniusrengta?ek2006-2010mokslai,metaisyVivi?lniusersitetas,univaersitete2Mokslinisdasvanaadoiusvunivas:ziniaiProf.matematikhabil.-dP)r.VofCon3ten.tsfsNotation.4.1.In.tro.ductionfor6Theorem1.1.Metricstic.....oisson...F...p.....non-iden...s...........27.......for.Pro.....for.s.........results.ariables.....e.1-dep.v.........236auxiliary1.2.P.oisson.t.ypforerunsappro.ximation.......35.sums.on.2.2.12.2.5.......46.yp.enden.i.........3.7...........1-dep.distributed.of.........t7ximatio1.3sumsKnotwndistributedresultss...................Pro.3.1...................Auxiliary.ound.ximations.....3.3.Theorems.................Auxiliary.ximations.analogue.en's.408of1.4.A.ctualit.y..........Auxiliary.oisson.appro.of.symmetric.t.ributio...................of...................3.8.sums.n.i.ernoulli.3.9.Theorems..........12.1.5.Thesis.structureoisson.yp.appro.n.for.of.enden.non-iden.ally.Bernoulli.ariable.......................................3.o.27.General.results..........16.2.Results.17.2.1.Comp.ound.P.oisson.appro.ximations.for.2-runs3.2sresultstatisticcomp.P.appro.for.statistic.......29.Pro.of.2.1.1.2.1.9..........17.2.2.Comp.ound.P.oisson.appro.ximations.for.sums.of3.41-depresultsendenapprotofrandomundervofariablesrankunderconditianalogue.of3.5FofrankTheoremsen's.condition..............................3.6.results.P.t.e.ximations.sums.1-dep.t.three.oin.d.st.n....20.2.3.P.oisson.t.yp.e.appro.ximations.for.sums.of.1-dep.enden.t.symmetric48threePropofoin2.3.1t.distri-.butions..............................50.Auxiliary.for.of.ende.t.t.cally.B.v.50.Pro.of.2.4.12.4.5..............................22552.4PN N =f1; 2;:::g
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k= 1
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itcM(t) = Mfkge M (t2R)k2Z
bEY Y 2Y1 k
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b bEY Y Y = EY Y Y EY Y EY Y ;1 2 k 1 2 k 1 j j+1 k
j=1
Y ;Y ;:::1 2
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