ON ERGODIC PROPERTIES OF NONLINEAR MARKOV CHAINS AND STOCHASTIC MCKEAN-VLASOV EQUATIONS

被引：41
作者：
Butkovsky, O. A. [1 ,2 ]
机构：
[1] Moscow MV Lomonosov State Univ, Dept Probabil Theory, Fac Math & Mech, Moscow 119991, Russia
[2] Technion Israel Inst Technol, IL-32000 Haifa, Israel
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2014年 / 58卷 / 04期
关键词：
nonlinear Markov processes; stochastic McKean-Vlasov equations; Dobrushin's condition; invariant measures; exponential convergence; NOISE; SDES;
D O I：
10.1137/S0040585X97986825
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study ergodic properties of nonlinear Markov chains and stochastic McKeanVlasov equations. For nonlinear Markov chains we obtain sufficient conditions for existence and uniqueness of an invariant measure and uniform ergodicity. We also prove optimality of these conditions. For stochastic McKean-Vlasov equations we establish exponential convergence of their solutions to stationarity in the total variation metric under Veretennikov-Khasminskii-type conditions.
引用
收藏
页码：661 / 674
页数：14
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