Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths

• 成果类型: Article
• 署名作者: Ancona, A; Lyons, R; Peres, Y
• 署名单位: Universite Paris Saclay; Indiana University System; Indiana University Bloomington; Hebrew University of Jerusalem; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677392
• 发表日期: 1999
• 页码: 970-989
• 关键词: graphs

摘要

Let {X-n} be a transient reversible Markov chain and let f be a function on the state space with finite Dirichlet energy. We prove crossing inequalities for the process (f(X-n)}(n greater than or equal to 1) and show that it converges almost surely and in L-2. Analogous results are also established for reversible diffusions on Riemannian manifolds.