GENERALIZED COUPLINGS AND ERGODIC RATES FOR SPDES AND OTHER MARKOV MODELS

• 成果类型: Article
• 署名作者: Butkovsky, Oleg; Kulik, Alexei; Scheutzow, Michael
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Wroclaw University of Science & Technology; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1485
• 发表日期: 2020
• 页码: 1-39
• 关键词: navier-stokes equations; unique ergodicity; subgeometric rates; harnack inequality; mixing properties; CONVERGENCE

摘要

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.