Reflecting random walk in fractal domains

Abstract

In this paper, we show that reflecting Brownian motion in any bounded domain D can be approximated, as $k\to \infty$, by simple random walks on "maximal connected" subsets of $(2^{-k}{\mathbb{Z}}^d)\cap D$ whose filled-in interiors are inside of D.

Published in at http://dx.doi.org/10.1214/12-AOP745 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Discrete approximations to reflected Brownian motion

Cited by in corpus (2)

• Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
• Markov chain approximations for one dimensional diffusions