Reflecting random walk in fractal domains

Krzysztof Burdzy; Zhen Qing Chen

doi:10.1214/12-AOP745

Reflecting random walk in fractal domains

Krzysztof Burdzy^*, Zhen Qing Chen

^*Corresponding author for this work

University of Washington

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, we show that reflecting Brownian motion in any bounded domain D can be approximated, as k→∞, by simple random walks on "maximal connected" subsets of (2^-kZ^d) n D whose filled-in interiors are inside of D.

Original language	English
Pages (from-to)	2791-2819
Number of pages	29
Journal	Annals of Probability
Volume	41
Issue number	4
DOIs	https://doi.org/10.1214/12-AOP745
Publication status	Published - 2013
Externally published	Yes

Keywords

Dirichlet form
Killed Brownian motion
Random walk
Reflected Brownian motion
Skorokhod space
Sobolev space
Tightness
Weak convergence

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10.1214/12-AOP745

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Burdzy, K., & Chen, Z. Q. (2013). Reflecting random walk in fractal domains. Annals of Probability, 41(4), 2791-2819. https://doi.org/10.1214/12-AOP745

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KW - Dirichlet form

KW - Killed Brownian motion

KW - Random walk

KW - Reflected Brownian motion

KW - Skorokhod space

KW - Sobolev space

KW - Tightness

KW - Weak convergence

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JF - Annals of Probability

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Reflecting random walk in fractal domains

Abstract

Keywords

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