Reflecting random walk in fractal domains
  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. 
Krzysztof Burdzy, Zhen-Qing Chen
math.PR