27570.由分?jǐn)?shù)布朗運(yùn)動(dòng)驅(qū)動(dòng)的隨機(jī)發(fā)展方程兩類問題的研究

1、StudyontwoproblemsonstochasticevolutionequationsdrivenbyfractionalBrownianmotionAbstractInthisthesiswemainlystudythefollowingtwoaspects.Ontheonehweconcernedwiththetimedependentstochasticevolutionequationsdrivenbyastardcy

2、lindricalWienerprocessanindependentcylindricalfractionalBrownianmotion(fBm)withHurstparameterHG(121)intheHilbertspacewithfinitedelayoftheform:!dx(t)=[A(t)x(t)f(tx(t—r⑴))]dtg(tx(t—u(t)))dW⑴a(t)dBH(t)tGJ:=[0T]⑴x(t)=沴(t)Tt0

3、.Weprovetheexistenceuniquenessofthemildsolutionsforthesystem(1)bymeansoftheBanachfixedpointtheorem.Anexampleisgiventoillustratetheresultofthiswork.Ontheotherhweconsidertheexistenceuniquenessofthemildsolutionforthefollowi

4、ngimpulsiveneutralstochasticfunctionalintegrodifferentialequationswithinfinitedelaydrivenbyastardWienerprocessanindependentfractionalBrownianmotion:d[x(t)g(txt)]=A[x(t)g(txt)]dt0B(t—s)[x(s)g(sxt)]dsf(txt)dth(txt)dw(t)cr(

5、t)dBQ(t)tGJ:=[0T]t=tk(2)Ax(tk)—x(t—xt——Ik(x(tk))k—12?、x⑴=^(t)GDfb0((—⑴0]x)tGJ0:=(―⑴0].WeprovetheexistenceuniquenessofthemildsolutionwiththecoefficientssatisfyingsomenonLipschitzconditionswhichincludetheclassicalLipschitz

6、conditionasspecialcase.Theresultisobtainedbyusingthemethodofsuccessiveapproximations.Anexampleisgiventoillustratetheresultofthiswork.Keywords:StochasticevolutionequationsevolutionoperatorfractionalBrownianmotionfixedpoin

7、ttheoremmildsolutionContentsAbstracti中文摘要iiChaper1Introduction11.1Background.............................................................................................11.2Preliminaries..................................

8、...........................................................31.2.1fractionalBrownianmotion........................................................31.2.2evolutionoperator....................................................

9、.....................51.2.3thephasespacepartialintegrodifferentialequationsinBanachspace............................................................................6Chaper2Ontimedependentstochasticevolutionequationsdrive

10、nbyfBminaHilbertspacewithfinitedelay82.1Themodel................................................................................................82.2Mainresult..............................................................

11、..................................92.3Anexample.............................................................................................14Chaper3Impulsiveneutralstochasticfunctionalintegrodifferentialequationswithinf

12、initedelaydrivenbyfBm163.1Themodel................................................................................................163.2Mainresult...........................................................................