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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 | |
| 引用本文： | 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. |
| 作者姓名： | 赵桂华 李春香 孙波 |
| 作者单位： | 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 |
| 基金项目： | 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）. |
| 摘 要： | 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. |
| 关 键 词： | 带跳随机微分方程 Euler-Maruyama 方法 几乎处处指数稳定性 均方指数稳定性 |
| 收稿时间： | 2013-04-25; |
ALMOST SURE AND MOMENT EXPONENTIAL STABILITIES OF EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS |
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| 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. | |
| Authors: | Zhao Guihua Li Chunxiang Sun Bo |
| Institution: | 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 |
| Abstract: | 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. |
| Keywords: | stochastic differential equation with jumps Euler-Maruyama method almost sure exponential stability mean-square exponential stability |
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