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A Skorobod-type lemma and a decomposition of reflected Brownian motion
(Institute of Mathematical Statistics, 1995-04)
We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.
On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions
(Birkhäuser Boston, Inc., 1989)
In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In particular, a necessary and sufficient condition was given for Brownian excursions in a Lipschitz domain to ...