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April 1999 Crossing Estimates and Convergence of Dirichlet Functions Along Random Walk and Diffusion Paths
Alano Ancona, Russell Lyons, Yuval Peres
Ann. Probab. 27(2): 970-989 (April 1999). DOI: 10.1214/aop/1022677392

Abstract

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 ${f (X _n)}_{n\geq 1}$ and show that it converges almost surely and in $L^2$. Analogous results are also established for reversible diffusions on Riemannian manifolds.

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Alano Ancona. Russell Lyons. Yuval Peres. "Crossing Estimates and Convergence of Dirichlet Functions Along Random Walk and Diffusion Paths." Ann. Probab. 27 (2) 970 - 989, April 1999. https://doi.org/10.1214/aop/1022677392

Information

Published: April 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0945.60063
MathSciNet: MR1698991
Digital Object Identifier: 10.1214/aop/1022677392

Subjects:
Primary: 60J45
Secondary: 31C25, 60F15

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 1999
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