Open Access
July 2013 Reflecting random walk in fractal domains
Krzysztof Burdzy, Zhen-Qing Chen
Ann. Probab. 41(4): 2791-2819 (July 2013). DOI: 10.1214/12-AOP745


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 $D$.


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Krzysztof Burdzy. Zhen-Qing Chen. "Reflecting random walk in fractal domains." Ann. Probab. 41 (4) 2791 - 2819, July 2013.


Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1286.60035
MathSciNet: MR3112932
Digital Object Identifier: 10.1214/12-AOP745

Primary: 60F17
Secondary: 31C25 , 46E35 , 60J10 , 60J60

Keywords: Dirichlet form , killed Brownian motion , Random walk , reflected Brownian motion , Skorokhod space , Sobolev space , tightness , weak convergence

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 4 • July 2013
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