| 随机延迟微分方程数值解的p阶矩指数稳定 |
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| 引用本文： | 范振成,刘明珠. 随机延迟微分方程数值解的p阶矩指数稳定[J]. 黑龙江大学自然科学学报, 2005, 22(4): 468-470 |
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| 作者姓名： | 范振成 刘明珠 |
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| 作者单位： | 哈尔滨工业大学,理学院,黑龙江,哈尔滨,150001;哈尔滨学院,数学系,黑龙江,哈尔滨,150086;哈尔滨工业大学,理学院,黑龙江,哈尔滨,150001 |
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| 基金项目： | 国家自然科学基金资助项目(10271036) |
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| 摘 要： | 尽管P阶矩指数稳定比P阶矩稳定更好,但迄今未见关于随机延迟微分方程数值解的P阶矩指数稳定的研究报导．此外在RAZUMIKHIN型定理已经被很好地应用于处理随机延迟微分方程解析解稳定性的同时,却没有随机延迟微分方程数值解的RAZUMIKHIN型结论．给出了随机延迟微分方程数值解的RAZUMIKHIN型P阶矩指数稳定条件;作为应用,考虑线性随机延迟微分方程的显式欧拉方法,得到了均方指数稳定条件．
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| 关 键 词： | 随机延迟微分方程 p阶矩指数稳定 均方指数稳定 |
| 文章编号： | 1001-7011(2005)04-0468-03 |
| 修稿时间： | 2004-12-20 |
The pth moment exponential stability for the stochastic delay differential equations |
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| FAN Zhen-cheng,LIU Ming-zhu. The pth moment exponential stability for the stochastic delay differential equations[J]. Journal of Natural Science of Heilongjiang University, 2005, 22(4): 468-470 |
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| Authors: | FAN Zhen-cheng LIU Ming-zhu |
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| Affiliation: | FAN Zhen - cheng,LIU Ming - zhu School of Science,Harbin Institute of Technology,Harbin 150001,China Department of Mathematics,Harbin College,Harbin 150086,China |
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| Abstract: | Although the pth moment exponential stability is more efficient than the pth moment stability, the research about the pth moment exponential stability of numerical solution of stochastic delay differential equations has not found. Moreover, the Razumikhin -type theorems have been well applied to the stability of stochastic delay differential equations. However, there is no result of Razumikhin type on the stability of numerical method for stochastic delay differential equations. The Razumikhin - type pth moment exponentially stable condition for the numerical solutions of stochastic differential equations is given. As application, the exponentially stable conditions in mean square are given for the explicit Euler methods applied to the linear stochastic delay differential equations. |
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| Keywords: | the stochastic delay differential equation the pth moment exponential stability the exponential stability in mean square |
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