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arXiv · 1907.03725

Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting

Oleg Butkovsky·Michael Scheutzow
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Abstract

We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence of transition probabilities of an order-preserving Markov process. As an application, we show exponential ergodicity and exponentially fast synchronization-by-noise of the stochastic reaction-diffusion equation in the hypoelliptic setting. This refines and complements corresponding results of Hairer, Mattingly (2011).

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Oleg Butkovsky, Michael Scheutzow. 2019-07-08. Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting. https://doi.org/10.1007/s00220-020-03834-w

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