中立型随机变延迟微分方程数值解的收敛性(英文)  

Convergence of numerical solutions to neutral stochastic delay differential equations with variable delay

作　　者：张玲[1,2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150008 [2]大庆师范学院数学科学学院,大庆163712

出　　处：《黑龙江大学自然科学学报》2012年第1期65-71,89,共8页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Youths’Key Projects of Heilongjiang Provincial Education Department(1155G001);he Youth Foundation of Daqing Normal University(09ZQ03)

摘　　要：讨论中立型随机变延迟微分方程欧拉方法的数值解的强收敛性。最近,很多作者已经对随机延迟微分方程的数值解进行了大量的研究,但是,对于中立型随机变延迟微分方程数值解收敛性的研究还很少。首先给出了中立型随机变延迟微分方程欧拉方法的数值格式,然后,在局部Lipschitz条件和有界条件下,论证了中立型随机变延迟微分方程欧拉方法的数值解收敛到解析解。The main purpose is to investigate the strong convergence of the Euler method to neutral stochastic delay differential equations（NSDDEs） with variable delay.Recently,numerical solutions of stochastic differential equations have received a great deal of attention.However,numerical solutions of neutral stochastic delay differential equations have received a little attention.A variant of the Euler-Maruyama method is used to define the numerical solutions for NSDDEs with variable delay.Then it is proved that the Euler approximation solution converge to the analytic solution of the NSDDEs with variable delay under the local Lipschitz condition and the bounded condition.

关 键 词：随机微分方程 中立型随机延迟微分方程 欧拉方法 变延迟 局部LIPSCHITZ条件 

分 类 号：O189.1[理学—数学]