On unique extension of time changed reflecting Brownian motions

Zhen Qing Chen; Masatoshi Fukushima

doi:10.1214/08-AIHP301

On unique extension of time changed reflecting Brownian motions

Zhen Qing Chen^*, Masatoshi Fukushima

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

Let D be an unbounded domain in ℝ^d with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1_D(x)m(x) dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.

源语言	英语
页（从-至）	864-875
页数	12
期刊	Annales de l'institut Henri Poincare (B) Probability and Statistics
卷	45
期	3
DOI	https://doi.org/10.1214/08-AIHP301
出版状态	已出版 - 8月 2009
已对外发布	是

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Chen, Z. Q., & Fukushima, M. (2009). On unique extension of time changed reflecting Brownian motions. Annales de l'institut Henri Poincare (B) Probability and Statistics, 45(3), 864-875. https://doi.org/10.1214/08-AIHP301

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abstract = "Let D be an unbounded domain in ℝd with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x) dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.",

keywords = "BL function space, Diffusion extension, Harmonic function, Reflected Dirichlet space, Reflecting Brownian motion, Sobolev space, Time change, Transience, Uniform domain",

author = "Chen, {Zhen Qing} and Masatoshi Fukushima",

year = "2009",

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doi = "10.1214/08-AIHP301",

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AU - Fukushima, Masatoshi

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N2 - Let D be an unbounded domain in ℝd with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x) dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.

AB - Let D be an unbounded domain in ℝd with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x) dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.

KW - BL function space

KW - Diffusion extension

KW - Harmonic function

KW - Reflected Dirichlet space

KW - Reflecting Brownian motion

KW - Sobolev space

KW - Time change

KW - Transience

KW - Uniform domain

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SN - 0246-0203

VL - 45

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

On unique extension of time changed reflecting Brownian motions

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