On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions

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On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions

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Title: On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions
Author: Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J.
Abstract: 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 share the local path properties with Brownian excursions in a half-space. This condition holds for C [to the power of 1, alpha] -domains ([alpha] > 0), but there is a C [to the power of 1]-domain for which it fails. Here we consider the distributions of a selection of local events for excursions. In particular, we focus on the asymptotics of these distributions as the region of locality shrinks to a point. We show that when a Lipschitz domain is locally approximated by a half-space, the asymptotics for excursions in the two domains are comparable.
URI: http://hdl.handle.net/1773/2248

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