高斯過程的局部時和隨機流動形.pdf

1、華中科技大學博士學位論文高斯過程的局部時和隨機流動形姓名：郭精軍申請學位級別：博士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：王才士王湘君20110523AbstractInrecentyearsfractionalBrownianmotion(fBm)hasbecomeanintenseobjectinstochasticanalysisrelatedfieldsfthemomentduetoitsinterestingpropertiessuc

2、hasselfsimilarityitsapplicationsinvariousscientificareas.HoweverwhenHurstparameterH?=12fBmisneitherasemimartingalenaMarkovianprocess.FBmcannotbedirectlydealtbymanymethodsresultsinstochasticanalysis.OntheotherhfBmmayberes

3、trictiveasamodel.IndertosimulatetherealsituationpreciselyitisurgentfustointroduceotherGaussianprocesses.TherefeitisinterestingchallengewktostudylocaltimesstochasticcurrentsoftheseGaussianprocesses.Inthispaperweusewhiteno

4、iseanalysisapproachMalliavincalculusmethodtostudythelocaltimesstochasticcurrentsoftheseGaussianprocesses.Themaininnovativeresultsofthispaperareasfollows.Insection3wediscussthelocaltimesofGaussianprocessesthroughwhitenois

5、eanalysisapproach.FirstlyprovethatthegeneralizedlocaltimeoftheWienerintegralwithrespecttoBrownianmotionisaHidadistribution.SecondlyfagivenpointcertifythatthelocaltimeoffBmisaHidadistributiongivethechaosexpansionoftheloca

6、ltimeintermsofmultipleIt?ointegral.SimilarresultsofddimensionfBmwithNparameterareresearched.WeobtainthechaosexpansionofthelocaltimeintermsofHermitepolynomial.ThirdlythemultipleintersectionlocaltimesoffBmareconsidered.Und

7、erthemildconditionsthemultipleintersectionlocaltimesoffBmareregardedasHidadistributions.FourthlythecollisionlocaltimesoftwoindependentfractionalBrownianmotionsareconsideredasHidadistributions.Underthemildconditionsgetthe

8、chaosexpansionsthekernelfunctionsoftwoindependentfractionalBrownianmotions.FinallytheresultsoftwoindependentfractionalBrownianmotionscanbeextendedtothecaseoftwoindependentmultifractionalBrownianmotionsthroughthesimilarme