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

Burdzy, Krzysztof; Williams, Ruth J.

doi:10.1090/S0002-9947-1986-0857445-2

On Brownian excursions in Lipschitz domains. I. Local path properties
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by Krzysztof Burdzy and Ruth J. Williams PDF

Trans. Amer. Math. Soc. 298 (1986), 289-306 Request permission

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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Local properties of

-dimensional Brownian excursions

Brownian excursions and minimal thinness

Applications to boundary behavior of the Green function

Brownian excursions and minimal thinness

Applications to the angular derivative problem

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