The method of parametric Lyapunov functions for Markov dynamic systems |
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Authors: | S M Dobrovol’skii T M Strugova |
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Institution: | (1) Omsk State University, ul. Neftezavodskaya 11, Omsk, 644077, Russia |
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Abstract: | The notion of parametric Lyapunov function is introduced for Markov dynamic systems. The existence of a function of this kind is shown to be a necessary and sufficient condition for the strong stochastic stability of an equilibrium. In terms of parametric Lyapunov functions, a sufficient criterion is proved for asymptotic strong stochastic stability in the case of Feller Markov chains. Some examples are given showing the efficiency of the method proposed. |
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