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.
Publié le : 1999-04-15
Classification:
Dirichlet energy,
random walk,
almost sure convergence,
Markov chain,
diffusions,
manifolds,
crossing,
60J45,
31C25,
60F15
@article{1022677392,
author = {Ancona, Alano and Lyons, Russell and Peres, Yuval},
title = {Crossing Estimates and Convergence of Dirichlet Functions Along
Random Walk and Diffusion Paths},
journal = {Ann. Probab.},
volume = {27},
number = {1},
year = {1999},
pages = { 970-989},
language = {en},
url = {http://dml.mathdoc.fr/item/1022677392}
}
Ancona, Alano; Lyons, Russell; Peres, Yuval. Crossing Estimates and Convergence of Dirichlet Functions Along
Random Walk and Diffusion Paths. Ann. Probab., Tome 27 (1999) no. 1, pp. 970-989. http://gdmltest.u-ga.fr/item/1022677392/