带跳变时滞随机微分方程E-M方法指数稳定性  

Exponential stability of E-M approximations of stochastic differential variable delay equations with jumps

作　　者：黄斌[1] 王拉省[1] 孙洁[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2008年第3期336-341,共6页Basic Sciences Journal of Textile Universities

基　　金：西安工程大学校管项目(2007XG32XGG07009)

摘　　要：研究了带跳变时滞随机微分方程Euler-Maruyama方法的指数稳定性.在全局Lipschitz条件及解析解和数值解在均方有界的条件下,证明了SDVDEJs的指数稳定性的充要条件是Eul-er-Maruyama方法下构造的数值解是指数稳定性.避免了寻找Lyapunov函数的困难,将指数稳定性的等价关系推广到带跳变时滞情形.The exponential stability of Euler-Maruyama method for the stochastic differential variable delay equation with jumps is mainly studied, The equivalence between exponential stability of exact solution and numerical solution which is constructed by Euler-Maruyama method is investigated under the condition that exact solution and numerical solution are both bounded in the meaning of Mean-square. The approach is trying to avoid the use of Lyapunov functions or functionals, and extend the main resuits to the jump case.

关 键 词：EULER-MARUYAMA方法 均方稳定 POISSON跳 Itō积分 指数稳定性 

分 类 号：O241.8[理学—计算数学]