On Ergodic Properties of Nonlinear Markov Chains and Stochastic McKean--Vlasov Equations

2014/01/01 by Oleg Butkovsky, O. A. Butkovsky · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Stochastic processes and financial applications

paper · doi:10.1137/s0040585x97986825

crossref issued 2014/01/01 · crossref published 2014/01/01 · crossref published-print 2014/01/01 · openalex publication_date 2014/01/01 · crossref created 2014/12/19 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31

Abstract

We study ergodic properties of nonlinear Markov chains and stochastic McKean--Vlasov 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.

Citations

• Central Limit Theorem for Nonstationary Markov Chains. I

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