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线性随机延迟积分微分方程Euler-Maruyama方法的稳定性

胡鹏, 黄乘明   

  1. 华中科技大学数学与统计学院, 武汉 430074
  • 收稿日期:2009-03-25 出版日期:2010-02-15 发布日期:2010-03-30
  • 基金资助:

    中国国家自然科学基金(No.10971077)

胡鹏, 黄乘明. 线性随机延迟积分微分方程Euler-Maruyama方法的稳定性[J]. 计算数学, 2010, 32(1): 105-112.

Hu Peng, Huang Chengming. STABILITY OF EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2010, 32(1): 105-112.

STABILITY OF EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Hu Peng, Huang Chengming   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2009-03-25 Online:2010-02-15 Published:2010-03-30
本文研究一类线性随机延迟积分微分方程Euler-Maruyama方法的MS-稳定性. 首先, 我们讨论方程真解的均方指数稳定性条件. 然后, 在此假设条件下,证明了带有复合梯形公式的Euler-Maruyama方法是MS-稳定的. 最后, 数值试验验证了本文的结论.

 

This paper is concerned with the MS-stability of Euler-Maruyama method for a class of linear stochastic delay integro-differential equations. First, we discuss the sufficient conditions of mean-square exponential stability for the true solution of these equations. And then, under such conditions, it is shown that the Euler-Maruyama method with composite trapezoidal rule is MS-stable. At last, we validate our conclusions by numerical experiments.

 

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[1] 王文强,黄山,李寿佛,. 非线性随机延迟微分方程Euler-Maruyama方法的均方稳定性[J]. 计算数学, 2007, 29(2): 217-224.
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