期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:260
Some contributions to stochastic asymptotic stability and boundedness via multiple Lyapunov functions
Article
Mao, XR
关键词: Lyapunov functions;    limit set;    supermartingale convergence theorem;    Ito's formula;   
DOI  :  10.1006/jmaa.2001.7451
来源: Elsevier
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【 摘 要 】

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper to establish some sufficient criteria: for locating the limit sets of solutions of stochastic differential equations. From them follow many useful results on stochastic asymptotic stability and boundedness, which enable us to construct the Lyapunov functions much more easily in applications. In particular, the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. These show clearly the power of our new results. (C) 2001 Academic Press.

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