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Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations

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  • Zhao, Guihua
  • Song, Minghui
  • Yang, Zhanwen

Abstract

From the view of algebra, the mean-square stability of analytic solutions and numerical solutions for impulsive stochastic differential equations are considered. By the logarithmic norm, the conditions under which the analytic and numerical solutions for a linear impulsive stochastic differential equation are mean-square stable (MS-stable) respectively are obtained. The conditions are simple and easy to use. Some numerical experiments are given to illustrate the results.

Suggested Citation

  • Zhao, Guihua & Song, Minghui & Yang, Zhanwen, 2015. "Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 527-538.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:527-538
    DOI: 10.1016/j.amc.2014.11.098
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    Cited by:

    1. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    2. Yu Zhang & Enying Zhang & Longsuo Li, 2022. "The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations," Mathematics, MDPI, vol. 10(18), pages 1-7, September.

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