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带跳随机微分方程的Euler-Maruyama方法的几乎处处指数稳定性和矩稳定性

赵桂华1, 李春香2, 孙波1   

  1. 1. 江苏科技大学数理学院, 江苏镇江 212000;
    2. 中国人民解放军第二军医大学数理教研室, 上海 200433
  • 收稿日期:2013-04-25 出版日期:2014-02-15 发布日期:2014-02-12
  • 基金资助:

    江苏省自然科学基金青年基金项目(BK20130472)、江苏科技大学博士启动基金(35050903)及校管科研课题项目(633051205).

赵桂华, 李春香, 孙波. 带跳随机微分方程的Euler-Maruyama方法的几乎处处指数稳定性和矩稳定性[J]. 计算数学, 2014, 36(1): 65-74.

Zhao Guihua, Li Chunxiang, Sun Bo. ALMOST SURE AND MOMENT EXPONENTIAL STABILITIES OF EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS[J]. Mathematica Numerica Sinica, 2014, 36(1): 65-74.

ALMOST SURE AND MOMENT EXPONENTIAL STABILITIES OF EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS

Zhao Guihua1, Li Chunxiang2, Sun Bo1   

  1. 1. Department of Mathematics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu, China;
    2. Department of Mathematics and Physics, Second Military Medical University, Shanghai 200433, China
  • Received:2013-04-25 Online:2014-02-15 Published:2014-02-12
本文首先研究了一维带跳随机微分方程的指数稳定性,并证明 Euler-Maruyama (EM)方法保持了解析解的稳定性.其次,研究了多维带跳随机微分方程的稳定性,证明若系数满足全局Lipchitz条件,则 EM 方法能够很好地保持解析解的几乎处处指数稳定性、均方指数稳定性. 最后,给出算例来支持所得结论的正确性.
First, the exponential stability for a scalar stochastic differential equation with jumps (SDEwJs) is studied. And, we show that Euler-Maruyama (EM) method reproduces the exponential stability of analytical solutions. Then, we study the stability for n-dimension SDEwJs. We show that EM method recovers almost sure exponential stability and meansquare exponential stability well under global Lipschtiz condition. Finally, some examples are provided to illustrate the results.

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