一般速率下马尔可夫调制随机系统的稳定性  

General Decay Stability of Stochastic Differential Equations with Markovian Switching

作　　者：邓飞其[1] 旷世芳[1] 赵学艳[1] 

机构地区：[1]华南理工大学自动化科学与工程学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2012年第10期102-108,共7页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61273126;60874114);广东省自然科学基金重点资助项目(10251064101000008)

摘　　要：一些稳定的随机系统是非指数稳定的,可能出现方程解收敛的速率较指数速率低的情况,如多项式或对数.为了更精确地定量分析系统的稳定性,文中将指数稳定概念推广到更一般稳定的衰减函数,研究了一类马尔可夫调制随机系统在一般衰减速率下的稳定性.利用It公式、Borel-Cantelli引理和鞅指数不等式等随机分析技巧,先建立了解析解p阶矩(t)稳定和几乎必然(t)稳定的定理,然后证明了在相同的条件下,对足够小的步长Δ,Euler Maruyama方法能保持相同的稳定性.It is worth pointing out that some stochastic systems are indeed stable but subject to a certain lower decay rate which is different from exponential decay, such as polynomial or logarithmic. For more accurate quantitative analyses of stability properties, this paper extends the usual exponential stability concepts to a more general stable decay function and investigates the general decay stability of stochastic differential equations with Markovian swit- ching. Firstly, some φ （t）-stability criteria in p-th moment and almost surely sense for the analytical solutions are established, by utilizing It6 formula, Borel-Cantelli and martingale exponential inequalities. Then the Euler Maru- yama method is shown to be effective in capturing φ（t）-stability behavior for all sufficiently small timesteps under appropriate conditions.

关 键 词：马尔可夫链 φ(t)稳定 EulerMaruyama方法 随机系统 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]