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

^*此作品的通讯作者

University of Washington

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	2791-2819
页数	29
期刊	Annals of Probability
卷	41
期	4
DOI	https://doi.org/10.1214/12-AOP745
出版状态	已出版 - 2013
已对外发布	是

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@article{7807ac790a134acd88358f99c92a5c5a,

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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pages = "2791--2819",

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TY - JOUR

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 - https://www.scopus.com/pages/publications/84881515814

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

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