On unique extension of time changed reflecting brownian motions

Zhen-Qing Chen; Masatoshi Fukushima

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 3, page 864-875
  • ISSN: 0246-0203

Abstract

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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∖̅B̅(̅0̅,̅ ̅r̅) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.

How to cite

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Chen, Zhen-Qing, and Fukushima, Masatoshi. "On unique extension of time changed reflecting brownian motions." Annales de l'I.H.P. Probabilités et statistiques 45.3 (2009): 864-875. <http://eudml.org/doc/78048>.

@article{Chen2009,
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&gt;0 so that D∖̅B̅(̅0̅,̅ ̅r̅) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.},
author = {Chen, Zhen-Qing, Fukushima, Masatoshi},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {reflecting brownian motion; transience; time change; uniform domain; Sobolev space; BL function space; reflected Dirichlet space; harmonic function; diffusion extension; reflecting Brownian motion},
language = {eng},
number = {3},
pages = {864-875},
publisher = {Gauthier-Villars},
title = {On unique extension of time changed reflecting brownian motions},
url = {http://eudml.org/doc/78048},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Chen, Zhen-Qing
AU - Fukushima, Masatoshi
TI - On unique extension of time changed reflecting brownian motions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 3
SP - 864
EP - 875
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&gt;0 so that D∖̅B̅(̅0̅,̅ ̅r̅) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that genuinely extends it and admits no killings.
LA - eng
KW - reflecting brownian motion; transience; time change; uniform domain; Sobolev space; BL function space; reflected Dirichlet space; harmonic function; diffusion extension; reflecting Brownian motion
UR - http://eudml.org/doc/78048
ER -

References

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