| 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. |
| 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 |
| DOI： |
| 分类号:O29 |
| 基金项目:Supported by NNSF (70871046) and HUST Foundation (0125011017). |
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| CONVERGENCE AND STABILITY OF NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL DELAY EQUATION |
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CHENG Sheng-min1, ZHOU Shao-bo2
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1.Department of Basic Teaching, Zhengzhou Huaxin College, Xinzheng 451100, China;2.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. |
| Key words: balanced method stochastic differential delay equation convergence mean-square stability asymptotic stability |
