| 随机中立型泛函微分方程的渐近性质 |
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| 引用本文： | 沈轶,张玉民,江明辉.随机中立型泛函微分方程的渐近性质[J].应用数学学报,2006,29(3):445-453. |
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| 作者姓名： | 沈轶 张玉民 江明辉 |
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| 作者单位： | 华中科技大学控制科学与工程系,武汉,430074 |
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| 基金项目： | 中国科学院资助项目;湖北省自然科学基金 |
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| 摘 要： | 本文研究了—般随机中立型泛函微分方程解的渐近性质,利用Lyapunov函数和半鞅收敛定理,建立了该方程解的一些渐近稳定性、多项式渐近稳定性及指数稳定性的充分性判据, 其条件无需算子LV负定,并且利用了随机扰动项在稳定性中所起的有益作用,其结果涵盖并推广了已有文献的结论．
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| 关 键 词： | 李雅普若夫函数 半鞅收敛定理 伊藤公式 渐近性质 |
| 收稿时间： | 2004-05-02 |
| 修稿时间： | 2004-05-022006-03-06 |
Asymptotic Properties of Neutral Stochastic Functional Differential Equations |
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| SHEN YI,ZHANG YUMIN,JIANG MINGHUI.Asymptotic Properties of Neutral Stochastic Functional Differential Equations[J].Acta Mathematicae Applicatae Sinica,2006,29(3):445-453. |
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| Authors: | SHEN YI ZHANG YUMIN JIANG MINGHUI |
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| Institution: | Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 |
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| Abstract: | The asymptotic properties of one type of neutral stochastic functional differential equations have been discussed in this paper. By Lyapunov function and semimartingale convergence theorem, some results on its properties such as asymptotic stabilities, polynomial stabilities and exponential stabilities have been given. The conditions need no negative -definite operator of LV, and the beneficial work of stochastic paterbation item on stability has been used well. All the results imply and generalize those conclusions existed in references. |
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| Keywords: | Lyapunov function semimartingale convergence theorem Ito^ formula asymptotic property |
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