A condition for the equivalence of coupling and shift coupling

• 成果类型: Article
• 署名作者: Cranston, M; Wang, FY
• 署名单位: University of Rochester; Beijing Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1666-1679
• 关键词: harmonic-functions; heat semigroups; continuous-time; kernel; MANIFOLDS

摘要

It is proved in this paper that a weak parabolic Harnack inequality for a Markov semigroup implies the existence of a coupling and a shift coupling for the corresponding process with equal chances of success. This implies equality of the tail and invariant sigma -fields for the diffusion as well as equality of the class of bounded parabolic functions and the class of bounded harmonic functions.