Generalized couplings and ergodic rates for SPDEs and other Markov models

By Oleg Butkovsky, A. Kulik, M. Scheutzow. The Annals of Applied Probability, 2018

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We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtained results to show exponential ergodicity of a variety of nonlinear stochastic partial differential equations with additive forcing, including 2D stochastic Navier-Stokes equations. Our main tool is a new version of the generalized coupling method.

Subfields: Computational Mechanics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a2d5d0dc039fbe6f125becbe1905342dede9d370