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Sibirskii Zhurnal Industrial'noi Matematiki, 2005, Volume 8, Number 3, Pages 40–47 (Mi sjim288)  
The method of parametric Lyapunov functions for Markov dynamical systems

S. M. Dobrovolskii, T. M. Strugova

Omsk State Technical University
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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.
Received: 20.01.2004
Revised: 12.05.2005
English version:
Journal of Applied and Industrial Mathematics, 2008, Volume 2, Issue 1, Pages 39–45
DOI: https://doi.org/10.1007/s11754-008-1005-2
Bibliographic databases:
UDC: 517.929:519.248
Language: Russian
Citation: S. M. Dobrovolskii, T. M. Strugova, “The method of parametric Lyapunov functions for Markov dynamical systems”, Sib. Zh. Ind. Mat., 8:3 (2005), 40–47; J. Appl. Industr. Math., 2:1 (2008), 39–45
Citation in format AMSBIB
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\paper The method of parametric Lyapunov functions for Markov dynamical systems
\jour Sib. Zh. Ind. Mat.
\yr 2005
\vol 8
\issue 3
\pages 40--47
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2220175}
\zmath{https://zbmath.org/?q=an:1100.60041}
\transl
\jour J. Appl. Industr. Math.
\yr 2008
\vol 2
\issue 1
\pages 39--45
\crossref{https://doi.org/10.1007/s11754-008-1005-2}
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