Open Access
February 2020 Generalized couplings and ergodic rates for SPDEs and other Markov models
Oleg Butkovsky, Alexei Kulik, Michael Scheutzow
Ann. Appl. Probab. 30(1): 1-39 (February 2020). DOI: 10.1214/19-AAP1485


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. "Generalized couplings and ergodic rates for SPDEs and other Markov models." Ann. Appl. Probab. 30 (1) 1 - 39, February 2020.


Received: 1 August 2018; Revised: 1 March 2019; Published: February 2020
First available in Project Euclid: 25 February 2020

zbMATH: 07200522
MathSciNet: MR4068305
Digital Object Identifier: 10.1214/19-AAP1485

Primary: 37L40 , 60H15 , 60J25

Keywords: ergodicity , generalized couplings , invariant measure , Markov processes , SPDEs

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 1 • February 2020
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