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Generalized couplings and ergodic rates for SPDEs and other Markov models. (English) Zbl 1434.60147

Summary: 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
60J25 Continuous-time Markov processes on general state spaces
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