非线性随机延迟微分方程Euler-Maruyama方法的均方稳定性  

MEAN-SQUARE STABILITY OF EULER-MARUYAMA METHODS FOR NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

作　　者：王文强[1] 黄山[1] 李寿佛[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《计算数学》2007年第2期217-224,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10271100);湖南省教育厅(06B091)资助项目.

摘　　要：本文首先将数值方法的均方稳定性的概念MS-稳定与GMS-稳定从线性试验方程推广到一般非线性的情形,然后针对一维情形下的非线性随机延迟微分方程初值问题,证明了如果问题本身满足零解是均方渐近稳定的充分条件,那么当漂移项满足一定的限制条件时,Euler- Maruyama方法是MS-稳定的与带线性插值的Euler-Maruyama方法是GMS-稳定的理论结果．In this paper, the authors investigated the mean-square stability of Euler- Maruyama methods for the nonlinear stochastic delay differential equations. At first, the both definitions of MS-stability and GMS-stability of numerical methods are developed from the linear scalar system to general case. And then, when the analytical solution satisfies the sufficient condition of the mean square stability, we obtained several theoretical results of Euler-Maruyama methods. If the drift term satisfies some restrictions, then Euler-Maruyama methods is MS-stable and Euler-Maruyama methods with linear interpolation is GMS-stable.

关 键 词：非线性随机延迟微分方程 Euler—Maruyama方法 MS-稳定性 GMS-稳定性 

分 类 号：O241.84[理学—计算数学]