Reflecting Brownian motion in a cusp
Authors:
R. Dante DeBlassie and Ellen H. Toby
Journal:
Trans. Amer. Math. Soc. 339 (1993), 297-321
MSC:
Primary 60J60; Secondary 60H99, 60J65
DOI:
https://doi.org/10.1090/S0002-9947-1993-1149119-1
MathSciNet review:
1149119
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the cusp
,
where
. Set
and
,
. We study the existence and uniqueness in law of reflecting Brownian motion in
. The angle of reflection at
(relative to the inward unit normal) is a constant
, and is positive iff the direction of reflection has a negative first component in all sufficiently small neighborhoods of 0. When
, existence and uniqueness in law hold. When
, existence fails. We also obtain results for a large class of asymmetric cusps. We make essential use of results of Warschawski on the differentiability at the boundary of conformal maps.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1993-1149119-1
Keywords:
Brownian motion with skew reflection,
cusp,
conformai transformation,
differentiability at the boundary
Article copyright:
© Copyright 1993
American Mathematical Society