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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On Brownian excursions in Lipschitz domains. I. Local path properties


Authors: Krzysztof Burdzy and Ruth J. Williams
Journal: Trans. Amer. Math. Soc. 298 (1986), 289-306
MSC: Primary 60J45; Secondary 60J65
MathSciNet review: 857445
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Abstract: A necessary and sufficient condition is given for a Brownian excursion law in a Lipschitz domain to share the local path properties with an excursion law in a halfspace. This condition is satisfied for all boundary points of every $ {C^{1,\alpha }}$-domain, $ \alpha > 0$. There exists a $ {C^1}$-domain such that the condition is satisfied almost nowhere on the boundary. A probabilistic interpretation and applications to minimal thinness and boundary behavior of Green functions are given.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857445-2
Keywords: Brownian motion, excursions, path properties, minimal thinness, Green functions, Lipschitz domains
Article copyright: © Copyright 1986 American Mathematical Society