Generalized couplings and convergence of transition probabilities

• 成果类型: Article
• 署名作者: Kulik, Alexei; Scheutzow, Michael
• 署名单位: National Academy of Sciences Ukraine; Institute of Mathematics of NASU; Technical University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0779-8
• 发表日期: 2018
• 页码: 333-376
• 关键词: navier-stokes equations; ergodicity

摘要

We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant measure. Our conditions are formulated in terms of generalized couplings. We apply our results to several SPDEs for which unique ergodicity has been proven in a recent paper by Glatt-Holtz, Mattingly, and Richards and show that under essentially the same assumptions the weak convergence of transition probabilities actually holds true.