| 随机延迟微分方程的数值方法的收敛性和稳定性 |
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| 引用本文： | 程生敏,周少波. 随机延迟微分方程的数值方法的收敛性和稳定性[J]. 数学杂志, 2014, 34(6): 1073-1084 |
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| 作者姓名： | 程生敏 周少波 |
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| 作者单位： | 郑州华信学院基础教学部;华中科技大学数学与统计学院; |
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| 基金项目： | Supported by NNSF(70871046);HUST Foundation(0125011017) |
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| 摘 要： | 本文研究了随机延迟微分方程的平衡方法的收敛性和均方稳定性.利用半鞅收敛定理,给出了真解的渐进稳定和均方稳定的一个更弱的条件.平衡方法下随机延迟微分方程的真解的均方稳定性.
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| 关 键 词： | 平衡方法 随机延迟微分方程 收敛性 均方稳定性 渐进稳定性 |
| 收稿时间： | 2013-05-13 |
| 修稿时间： | 2013-09-05 |
CONVERGENCE AND STABILITY OF NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL DELAY EQUATION |
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| CHENG Sheng-min and ZHOU Shao-bo. CONVERGENCE AND STABILITY OF NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL DELAY EQUATION[J]. Journal of Mathematics, 2014, 34(6): 1073-1084 |
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| Authors: | CHENG Sheng-min and ZHOU Shao-bo |
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| Affiliation: | Department of Basic Teaching, Zhengzhou Huaxin College, Xinzheng 451100, China and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | The paper investigates convergence and mean-square stability of the balanced method for stochastic differential delay equation. By applying the semi-martingale convergence theorem, a weaker condition of asymptotic and mean-square stability of the exact solution is given, the balanced method reproduces mean-square stability of the exact solution for stochastic differential delay equation. |
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| Keywords: | balanced method stochastic differential delay equation convergence mean-square stability asymptotic stability |
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