Generalized couplings and ergodic rates for SPDEs and other Markov models

Oleg Butkovsky; Alexei Kulik; Michael Scheutzow

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arXiv · 1806.00395

Generalized couplings and ergodic rates for SPDEs and other Markov models

Oleg Butkovsky·Alexei Kulik·Michael Scheutzow

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Abstract

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.

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Oleg Butkovsky, Alexei Kulik, Michael Scheutzow. 2018-06-01. Generalized couplings and ergodic rates for SPDEs and other Markov models. https://arxiv.org/abs/1806.00395

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