| 随机微分方程Milstein方法的稳定性 |
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| 引用本文： | 朱霞,李建国,李宏智,姜珊珊.随机微分方程Milstein方法的稳定性[J].华中科技大学学报(自然科学版),2003,31(3):111-113. |
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| 作者姓名： | 朱霞 李建国 李宏智 姜珊珊 |
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| 作者单位： | 华中科技大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目 ( 699740 1 8) . |
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| 摘 要： | 基于随机微分方程的两类试验方程，即噪声为增加噪声和附加噪声的两种情况，讨论了求解标量自治随机微分方程的Milstein数值方法的三种稳定性：A-稳定性、均方稳定性和T-稳定性．得出确定性情形的A-稳定性延伸到随机性情形时保持不变的结论，给出了当试验方程的参数为实数时方法的均方稳定域．
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| 关 键 词： | 随机微分方程 Milstein数值方法 均方稳定性 A-稳定性 T-稳定性 |
| 文章编号： | 1671-4512(2003)03-0111-03 |
| 修稿时间： | 2002年10月13 |
The stability properties of Milstein scheme for stochastic differential equations |
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| Zhu Xia Li Jianguo Li Hongzhi Jiang ShanshanZhu Xia Postgraduate, Dept. of Math. Huazhong Univ. of Sci. & Tech.,Wuhan ,China..The stability properties of Milstein scheme for stochastic differential equations[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2003,31(3):111-113. |
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| Authors: | Zhu Xia Li Jianguo Li Hongzhi Jiang ShanshanZhu Xia Postgraduate Dept of Math Huazhong Univ of Sci & Tech Wuhan China |
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| Institution: | Zhu Xia Li Jianguo Li Hongzhi Jiang ShanshanZhu Xia Postgraduate, Dept. of Math. Huazhong Univ. of Sci. & Tech.,Wuhan 430074,China. |
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| Abstract: | Based on the two types of test equations of stochastic differential equations, additive noise and multiplicative noise, the stability of Milstein numerical scheme for autonomous scalar stochastic differential equations such as the mean square stability, A stability and T stability was studied. It was shown that an extension of the deterministic A stability property holds. The figures of the mean square stability regions were presented for the case when the test equations have real parameters. |
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| Keywords: | stochastic differential equations Milstein numerical scheme mean square stability A stability T stability |
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