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.
Publié le : 2009-08-15
Classification:
Reflecting Brownian motion,
Transience,
Time change,
Uniform domain,
Sobolev space,
BL function space,
Reflected Dirichlet space,
Harmonic function,
Diffusion extension,
60J50,
60J60
@article{1249391389,
author = {Chen, Zhen-Qing and Fukushima, Masatoshi},
title = {On unique extension of time changed reflecting Brownian motions},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 864-875},
language = {en},
url = {http://dml.mathdoc.fr/item/1249391389}
}
Chen, Zhen-Qing; Fukushima, Masatoshi. On unique extension of time changed reflecting Brownian motions. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 864-875. http://gdmltest.u-ga.fr/item/1249391389/