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

By Oleg Butkovsky. 2013

72 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/23be3ba8ca1aa91005f51bb18590a738cf0abef4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Raphael Zimmer
2. Arnaud Guillin
3. Andreas Eberle

In Finance

1. Andreas Eberle
2. Raphael Zimmer
3. Arnaud Guillin
4. Mateusz B. Majka

In Statistical and Nonlinear Physics

1. Andreas Eberle
2. Raphael Zimmer
3. Arnaud Guillin

Citations in the corpus

• Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, methodology): “The approach in [7] yields exponential convergence to equilibrium in total variation distance in the small and bounded interaction case.”