Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths
type: Item
instance of: scholarly article
title: Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths
zbMATH Open document ID: 0945.60063
author: Alano Ancona
author: Russell Lyons
author: Yuval Peres
published in: The Annals of Probability
publication date: 1999-11-09T00:00:00Z
review text: The authors establish a crossing estimate for a Dirichlet function \(f\) along the path of a transient reversible Markov chain \(\{X_n\}\) and prove that the process \(\{f(X_n)\): \(n\geq 1\}\) converges almost surely and in \(L^2\). Similar results are also established for a transient symmetric diffusion on a Riemannian manifold. Results on crossing estimates are recently generalized to symmetric right Markov processes by \textit{Z.-Q. Chen, P. Fitzsimmons} and \textit{R. Song} [``Crossing estimates for symmetric Markov processes''].
reviewed by: Zoran Vondraček
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 1359660
zbMATH Keywords: Dirichlet energy
zbMATH Keywords: random walk
zbMATH Keywords: almost sure convergence
zbMATH Keywords: Markov chain
zbMATH Keywords: diffusions
zbMATH Keywords: manifolds
zbMATH Keywords: crossing
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022677392
OpenAlex ID: W2032573808
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DOI: 10.1214/AOP/1022677392
description: scientific article; zbMATH DE number 1359660