随机延迟微分方程的Milstein方法的均方稳定性

随机延迟微分方程的Milstein方法的均方稳定性 Mean-Square Stability of the Milstein Method for Stochastic Delay Differential Equations 朱霞 ZHU Xia 1 first-author 中南财经政法大学信息学院,湖北,武汉,430060 中南财经政法大学信息学院,湖北,武汉,430060 School of Information,Zhongnan University of Economics and Law School of Information,Zhongnan University of Economics and Law 研究随机延迟微分方程（stochastic delay differential equations）的数值求解问题,将改造后的Milstein方法用于求解此类问题,精度较高.对一切满足理论解均方（Mean-Square）稳定的系统,事实证明由上述方法离散得到的数值解不需任何附加条件即可保持与系统相同的稳定性.数值实验也直观地验证了所得的结论. This paper investigates the adapted Milstein method for solving linear stochastic delay differential equations（SDDEs）.It is proved that the numerical method is Mean-Square（MS） stable under suitable conditions.The obtained result shows that the method preserves the stability property of the solved system.This is also verified by several numerical examples. 随机延迟微分方程 均方稳定 Milstein方法 数值解 stochastic delay differential equations mean-square stability Milstein method numerical solution O211.63 2005-01-01 2021-04-01 S2