Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets

Z. Q. Chen; P. J. Fitzsimmons; R. J. Williams

doi:10.1007/BF01048506

Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets

Z. Q. Chen^*, P. J. Fitzsimmons, R. J. Williams

^*Corresponding author for this work

University of California at San Diego

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

26 Citations (Scopus)

Abstract

A notion of strong Caccioppoli set is defined for bounded Euclidean domains. It is shown that stationary (normally) reflecting Brownian motion on the closure of a bounded Euclidean domain is a quasimartingale on each compact time interval if and only if the domain is a strong Caccioppoli set. A similar result is shown to hold for symmetric reflecting diffusion processes.

Original language	English
Pages (from-to)	219-243
Number of pages	25
Journal	Potential Analysis
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/BF01048506
Publication status	Published - Sept 1993
Externally published	Yes

Keywords

Brownian motion
Caccioppoli set
Dirichlet form
Mathematics Subject Classifications (1991): Primary 60J65, secondary 60J60, 60J55, 49Q15, 31C25
Skorokhod decomposition
quasimartingale
reflecting symmetric diffusion
set of finite perimeter

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abstract = "A notion of strong Caccioppoli set is defined for bounded Euclidean domains. It is shown that stationary (normally) reflecting Brownian motion on the closure of a bounded Euclidean domain is a quasimartingale on each compact time interval if and only if the domain is a strong Caccioppoli set. A similar result is shown to hold for symmetric reflecting diffusion processes.",

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author = "Chen, {Z. Q.} and Fitzsimmons, {P. J.} and Williams, {R. J.}",

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AU - Fitzsimmons, P. J.

AU - Williams, R. J.

PY - 1993/9

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AB - A notion of strong Caccioppoli set is defined for bounded Euclidean domains. It is shown that stationary (normally) reflecting Brownian motion on the closure of a bounded Euclidean domain is a quasimartingale on each compact time interval if and only if the domain is a strong Caccioppoli set. A similar result is shown to hold for symmetric reflecting diffusion processes.

KW - Brownian motion

KW - Caccioppoli set

KW - Dirichlet form

KW - Mathematics Subject Classifications (1991): Primary 60J65, secondary 60J60, 60J55, 49Q15, 31C25

KW - Skorokhod decomposition

KW - quasimartingale

KW - reflecting symmetric diffusion

KW - set of finite perimeter

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SP - 219

EP - 243

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets

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Keywords

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