中立型线性随机延迟微分方程的Euler-Maruyama方法的渐近均方稳定性(英文)  

AMS-stability of the Euler-Maruyama method for linear neutral stochastic delay differential equations

作　　者：周立群[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《黑龙江大学自然科学学报》2013年第4期445-452,457,共9页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundation of China(60974144);the Foundation for Doctors of Tianjin Normal university(52LX34);Development Program in the Science Research Project for Colleges and Universities of Tianjin of China(20100813)

摘　　要：研究中立型线性随机延迟微分方程的Euler-Maruyama方法的渐近均方稳定性。建立数值方法渐近均方稳定性的定义,给出Euler-Maruyama方法的渐近均方稳定的充分条件,并证明在这些条件下中立型线性随机延迟微分方程的Euler-Maruyama方法是渐近均方稳定的,给出了支持所得结果的数值算例。Stability of Euler-Maruyama method for linear neutral stochastic delay differential equations is considered. The definition of asymptotic mean square （AMS）-stability of numerical methods is established. The conditions of asymptotic mean square stability of Euler-Maruyama methods for the system are given. It is shown that the Euler-Maruyama method is AMS-stable under these conditions. The numerical examples are presented to support the obtained results.

关 键 词：中立型随机延迟微分方程 渐近均方稳定性 Euler—Maruyama方法 数值解 方差 

分 类 号：O241.8[理学—计算数学]