Geodesic
The method of parametric Lyapunov functions for Markov dynamical systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 40-47 
S. M. Dobrovolskii; T. M. Strugova. The method of parametric Lyapunov functions for Markov dynamical systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 40-47. http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a5/
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     author = {S. M. Dobrovolskii and T. M. Strugova},
     title = {The method of parametric {Lyapunov} functions for {Markov} dynamical systems},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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