随机微分包含数值解的收敛性-论文.pdf

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1、第31卷第3期黑龙江大学自然科学学报Vol_3lNo．32014年6月JOURNALOFNATURALSCIENCEOFHEILONGJ‘IANGUNIVERSITYJune，2014DOI：10．13482／j．issnl001—7011．2014．01．240ConvergenceofnumericalsolutionsforstochasticdifferentialinclusionsZHANGLing(InstituteofMathematicalSciences，DaqingNormalUniversity，Daqing163712，China)Abstract：Th

2、emainpurposeistoinvestigatethestrongconvergenceoftheEulermethodtostochas‘ticdifferentialinclusions(SDIs)underglobalLipschitzconditionandthelineargrowthcondition．ItisfirstshownthatSDIswiththeinitialvaluehaveasolutionunderglobalLipschitzconditionandthelineargrowthcondition．Thentheconvergenceofn

3、umericalsolutionstoSDIsunderthesameconditionsisestab—lished．Finally，anexampleisprovidedtoillustratethetheoryresults．Keywords：stochasticdifferentialinclusion；thelineargrowthcondition；globalLipschitzcondi-tion；Hausdoffmetric；Euler—MaruyamamethodCLCnumber：O189．1Documentcode：AArticleID：1001—7011(

4、2014)03—0344—07随机微分包含数值解的收敛性张玲(大庆师范学院数学科学学院，大庆163712)摘要：讨论在全局Lipschitz条件和线性增长条件下，随机微分包含欧拉方法的数值解的强收敛性。给出在同样条件下随机微分包含解的存在性，以及随机微分包含欧拉方法的数值格式，证明在全局Lipschitz条件和线性增长条件下，随机微分包含欧拉方法的数值解收敛到解析解。数值实例验证了结论的正确性。关键词：随机微分包含；线性增长条件；全局Lipschitz条件；Hausdrof距离；欧拉方法0IntroductionStochasticmodelinghascometoplayani

5、mportantroleinmanybranchesofscienceandindustry．SuchmodelshavebeenusedwithgreatSuccessinavarietyofapplicationareas，includingbiology，epidemiology，mechanics，e—conomicsandfinance．Moststochasticdifferentialequations(SDEs)arenonlinearandcannotbesolvedexplicitly，butitisveryimportanttoresearchtheexis

6、tenceanduniquenessofsolutionofSDEs．ManyauthorshavestudiedtheproblemforSDEsL1-31．Similarly．theclassicalexistence—and—uniquenesstheoremforstochasticdifferentialdelaye—quations(SDDEs)areestablishedbymanyauthors“tO]．However，inmanypracticalproblems，theexistenceofaReceiveddate：2013—11一o4Foundationi

7、tem：SupposedbytheScienceandTechnologyResearchPr~eetsofHeilongjiangProvincialEducationDepartment(11553003)；theResearchFundfortheDoctoralProgramofDaqingNormalUniversityBiography：Ms．ZHANGLing(1978一)，Lecturer，Ph．D．，interestedin：computationalmathe