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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title = "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→∞, by simple random walks on {"}maximal connected{"} subsets of (2-kZd) n D whose filled-in interiors are inside of D.",

keywords = "Dirichlet form, Killed Brownian motion, Random walk, Reflected Brownian motion, Skorokhod space, Sobolev space, Tightness, Weak convergence",

author = "Krzysztof Burdzy and Chen, {Zhen Qing}",

year = "2013",

doi = "10.1214/12-AOP745",

language = "English",

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T1 - Reflecting random walk in fractal domains

AU - Burdzy, Krzysztof

AU - Chen, Zhen Qing

PY - 2013

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N2 - 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-kZd) n D whose filled-in interiors are inside of D.

AB - 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-kZd) n D whose filled-in interiors are inside of D.

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

UR - http://www.scopus.com/inward/record.url?scp=84881515814&partnerID=8YFLogxK

U2 - 10.1214/12-AOP745

DO - 10.1214/12-AOP745

M3 - Article

AN - SCOPUS:84881515814

SN - 0091-1798

VL - 41

SP - 2791

EP - 2819

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Reflecting random walk in fractal domains

Abstract

Keywords

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