Journal of South China University of Technology(Natural Science Edition) ›› 2012, Vol. 40 ›› Issue (10): 102-108.doi: 1000-565X(2012)10-0102-07

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General Decay Stability of Stochastic Differential Equations with Markovian Switching

Deng Fei-qi  Kuang Shi-fang  Zhao Xue-yan   

  1. School of Automation Science and Engineering,South China University of Technology,Guangzhou 510640,Guangzhou,China
  • Received:2012-07-30 Online:2012-10-25 Published:2012-09-01
  • Contact: 邓飞其(1962-) ，男，教授，博士生导师，主要从事随机系统建模、分析与控制理论、系统工程等的研究． E-mail:aufqdeng@ scut.edu.cn
  • About author:邓飞其(1962-) ，男，教授，博士生导师，主要从事随机系统建模、分析与控制理论、系统工程等的研究．
  • Supported by:

    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)

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Abstract:

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 switching. Firstly,some φ( t) -stability criteria in p-th moment and almost surely sense for the analytical solutions are established,by utilizing ItÔ formula,Borel-Cantelli and martingale exponential inequalities. Then the Euler Maruyama method is shown to be effective in capturing φ( t) -stability behavior for all sufficiently small timesteps under appropriate conditions.

Key words: Markov chain, φ( t) -stability, Euler Maruyama method, stochastic systems