标量随机延迟微分方程Euler-Maruyama方法的均方稳定性分析

广东工业大学学报 ›› 2011, Vol. 28 ›› Issue (1): 50-53.

标量随机延迟微分方程Euler-Maruyama方法的均方稳定性分析

广东工业大学应用数学学院，广东广州 510006

出版日期:2011-12-25 发布日期:2011-12-25
作者简介:王琦(1978-)，男，讲师，博士研究生，主要研究方向为微分方程数值解.
基金资助:
广东省自然科学基金资助项目(9451009001002753);广东工业大学青年基金资助项目(092027)

Mean-Square Stability Analysis of EulerMaruyama Method for Scalar Stochastic Delay Differential Equations

Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Online:2011-12-25 Published:2011-12-25

摘要/Abstract

摘要： 在解析解均方稳定的条件下研究带有乘性噪声的标量随机延迟微分方程EulerMaruyama方法的均方稳定性.证明了当步长满足一定限制时,数值解是均方稳定的.数值算例验证了理论结果的正确性.
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关键词: 随机延迟微分方程;EulerMaruyama方法;均方稳定性

Abstract: Mean-square stability of EulerMaruyama method is studied for scalar stochastic delay differential equations with multiplicative noise under the condition of analytical meansquare stability.It is proven that the numerical solution is meansquare stable when the stepsize satisfies certain restrictions.Numerical examples verify the theoretical results.

Key words: stochastic delay differential equations; Euler-Maruyama method; mean-square stability

王琦. 标量随机延迟微分方程Euler-Maruyama方法的均方稳定性分析[J]. 广东工业大学学报, 2011, 28(1): 50-53.

WANG Qi. Mean-Square Stability Analysis of EulerMaruyama Method for Scalar Stochastic Delay Differential Equations[J]. Journal of Guangdong University of Technology, 2011, 28(1): 50-53.

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