| 随机延迟微分方程的Milstein方法的非线性均方稳定性 |
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| 引用本文： | 王志勇,张诚坚. 随机延迟微分方程的Milstein方法的非线性均方稳定性[J]. 应用数学, 2008, 21(1): 201-206 |
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| 作者姓名： | 王志勇 张诚坚 |
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| 作者单位： | 华中科技大学数学系,湖北,武汉,430074 |
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| 摘 要： | 本文针对一般的非线性随机延迟微分方程,证明了当系统理论解满足均方稳定性条件时,则当方程的漂移和扩散项满足一定的条件时,Milstein方法也是均方稳定的.数学实验进一步验证了我们的结论.
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| 关 键 词： | 随机延迟微分方程 均方稳定 Milstein方法 数值解 随机延迟微分方程 方法 非线性 均方稳定性 Delay Differential Equations Stochastic Nonlinear Method 验证 数学实验 定性条件 扩散项 漂移 理论解 系统 |
| 文章编号： | 1001-9847(2008)01-0201-06 |
| 修稿时间： | 2007-06-27 |
Mean-Square Stability of Milstein Method for Solving Nonlinear Stochastic Delay Differential Equations |
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| WANG Zhi-yong,ZHANG Cheng-jian. Mean-Square Stability of Milstein Method for Solving Nonlinear Stochastic Delay Differential Equations[J]. Mathematica Applicata, 2008, 21(1): 201-206 |
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| Authors: | WANG Zhi-yong ZHANG Cheng-jian |
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| Abstract: | We investigated the mean-square stability of Milstein method for nonlinear stochastic delay differential equations.When the analytical solution satisfies the conditions of mean-square stability,and if the drift term and diffusion term satisfy some restrictions,then the Milstein method is mean-square stable.This is also verified by several numerical examples. |
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| Keywords: | Stochastic delay differential equations Mean-square stability Milstein method Numerical solution |
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