马尔科夫切换型中立型随机泛函微分方程被引量：1

Neutral Stochastic Functional Differential Equations with Markovian Switchings

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摘要尽管具有马尔科夫切换型随机微分方程的稳定性受到了人们的关注,但是关于具有马尔科夫切换型中立型随机泛函微分方程的稳定性的研究则很少.本文的主要目的是试图研究这一问题,我们证明了解的存在唯一性,并得到了p-阶指数稳定性和几乎处处指数稳定性的判据. The stability of stochastic functional differential equation with Markovian switching have an increasing attention, but there is almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching. The main aim of this paper is to close this gap. We establishes the existence and uniqueness of the neutral stochastic functional differential equations with Markovian switching, and obtain criteria for p-th moment exponential stability and almost surely exponential stability for the solutions.

作者周少波

机构地区华中科技大学数学与统计学院

出处《应用数学学报》 CSCD 北大核心 2012年第6期1128-1140,共13页 Acta Mathematicae Applicatae Sinica

基金国家自然科学基金(70871046) 华中科技大学自主创新基金(2011QN167)资助项目

关键词马尔科夫链布朗运动中立型随机泛函微分方程指数稳定性 Markovian chain Brownian motion neutral stochastic functional differential equation exponential stability

分类号 O212.7 [理学—概率论与数理统计]

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参考文献7

1Mao X R. Stability of Stochastic Differential Equations with Maxkovian Switching. Stochastic Pro- cesses and their Applications, 1999, 79:45-67.
2Mao X R, Matasav A, Piunovskiy A. Stochastic diefferential delay equation with Markovian Switching. Bernoulli, 2000, 6(1): 73-90.
3Mao X R. Robustness of Stability of Stochastic Differential Delay Equations with Markovian Switching Stability and Control: Theory Applications, 2000, 3(1): 48-61.
4Mao X R. Stochastic Functional Differential Equations with Markovian Switching. Functional Dif- ferential Equations, 1999, 6:375-396.
5] Kolmanovskii V, Koroleva N, Maizenberg T, Mao X R, Matasov A. Neutral Stochastic Differential Delay Equation with Markovian Switching. Stochastic Analysis and Application, 2003, 21(4): 839-867.
6Skorohod A V. Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence: American Mathematical Society, 1989.
7Mao X R. Stochastic Differential Equations and Applications. Horword, Chichester, UK, 2008.