随机泛函微分系统的渐近性分析-论文.pdf

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1、第3O卷第3期大学数学Vo1．3O，№．32014年6月C0LLEGEMATHEMATICSJun．2014AsymptoticPropertyofNonlinearStochasticFunctiona1DifferentialSystemsZHoUShao-bo，XUSheng(sch00l0fMathematicsandStatistics，HuazhongUniversityofScienceandTehcnology，Wuhan430074，China；Schoo1ofManagement，HefeiUniversityofTechnolog

2、y，Hefei230009，China)Abstract：Wewillestablishnewresultsonasymptoticstabilityforstochasticfunctionaldifferentialsystems．MostoftheexistingcriteriaonstabilityrequirethecoefficientstoobeYthelineargrowthcondition·Themainaimofthepaperistoremovetherestrictivecondition．Ournewcriterianoto

3、nlycovermanyhighlyn0nlinearst0chasticfunetionaldifferentialsystem，buttheycanalsobeverifiedmuchmoreeasilythantheexistingcriteria．Keywords：nonlinearst0chasticfunctiona1d册erentia1systems；Brownianmotion，asymptoticstability；momentstability；LyapunovfunctionsCLCNumber：DocumentCode：AArt

4、icleID：1672-1454(2014)03—0001—091IntroductionStochasticmodelinghasplayedanimportantroleinmanyareasofscienceandengineeringfora1ongtime．Someofthem‘)stfrequentandmostimportantstochasticmodelsusedwhendynamicolsystemsdependnotonlyonpresentandpaststatesbutalsoinvolvederivativeswithfun

5、ctionals，aredescribedbyverycomplexneutralstochasticfunctionaldifferentialequationsd[z()-u(x，t)-I一，(，t)dt+g(x，t)dw(t)．(1．1)KolmanovskiiandNosov[1]，MiljanaandSvetlana[2]，Mao[3]，SveltanaandZhou‘5have．estabnshedexponentialstaI)ilitycriteriaofneutralstochasticfunctionaldifferentialeq

6、uation·Thekeyconditi0nsimposedontheirstudiesarethestandardlocalLipschitzconditionandthelineargrowthcondti0n．However，therearemanystochasticfunctionaldifferentialequationwhichdoobeythelineargrowthcondti0n．Forexample，considerascalarstochasticfunctionaldifferentialequationdIz(￡)一cI(

7、)()一-ax()d+IP专()(O)dOdw(t)，(1·2)LJ—r一‘where硼(￡)isascalarBrownmotion．Obviously，coefficientsf(xf，￡)andg(xt’￡)donottythelineargrowthconditionalthoughtheyareLipschitzcontinuous．Wewonderwhetherthenonolinearstochasticfunctiona1differentialequationisexponentiallystable．Tothebestknown1e

8、dge，therearerecentlyafewauthorswhostudiedasympt