Geodesic
The method of parametric Lyapunov functions for Markov dynamical systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 40-47

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. 
@article{SJIM_2005_8_3_a5,
     author = {S. M. Dobrovolskii and T. M. Strugova},
     title = {The method of parametric {Lyapunov} functions for {Markov} dynamical systems},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {40--47},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a5/}
}
TY  - JOUR
AU  - S. M. Dobrovolskii
AU  - T. M. Strugova
TI  - The method of parametric Lyapunov functions for Markov dynamical systems
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2005
SP  - 40
EP  - 47
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a5/
LA  - ru
ID  - SJIM_2005_8_3_a5
ER  - 
%0 Journal Article
%A S. M. Dobrovolskii
%A T. M. Strugova
%T The method of parametric Lyapunov functions for Markov dynamical systems
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2005
%P 40-47
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a5/
%G ru
%F SJIM_2005_8_3_a5
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/