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

^*此作品的通讯作者

University of California at San Diego

科研成果: 期刊稿件 › 文章 › 同行评审

26 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	219-243
页数	25
期刊	Potential Analysis
卷	2
期	3
DOI	https://doi.org/10.1007/BF01048506
出版状态	已出版 - 9月 1993
已对外发布	是

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Chen, Z. Q., Fitzsimmons, P. J., & Williams, R. J. (1993). Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets. Potential Analysis, 2(3), 219-243. https://doi.org/10.1007/BF01048506

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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.

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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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JO - Potential Analysis

JF - Potential Analysis

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ER -

Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets

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