Boundary trace of reflecting Brownian motions

Itai Benjamini; Zhen Qing Chen; Steffen Rohde

doi:10.1007/s00440-003-0318-7

Boundary trace of reflecting Brownian motions

Itai Benjamini^*, Zhen Qing Chen, Steffen Rohde

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Probability Theory and Related Fields
Volume	129
Issue number	1
DOIs	https://doi.org/10.1007/s00440-003-0318-7
Publication status	Published - May 2004
Externally published	Yes

Keywords

Boundary occupation time
Boundary trace
Conformal mapping
Hausdorff dimension
Reflecting Brownian motion
Uniform dimensional result

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10.1007/s00440-003-0318-7

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Benjamini, I., Chen, Z. Q., & Rohde, S. (2004). Boundary trace of reflecting Brownian motions. Probability Theory and Related Fields, 129(1), 1-17. https://doi.org/10.1007/s00440-003-0318-7

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abstract = "We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.",

keywords = "Boundary occupation time, Boundary trace, Conformal mapping, Hausdorff dimension, Reflecting Brownian motion, Uniform dimensional result",

author = "Itai Benjamini and Chen, {Zhen Qing} and Steffen Rohde",

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AU - Chen, Zhen Qing

AU - Rohde, Steffen

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AB - We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.

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KW - Boundary trace

KW - Conformal mapping

KW - Hausdorff dimension

KW - Reflecting Brownian motion

KW - Uniform dimensional result

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M3 - Article

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VL - 129

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

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ER -

Boundary trace of reflecting Brownian motions

Abstract

Keywords

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