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Transactions of the American Mathematical Society

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



Brownian excursions from hyperplanes and smooth surfaces

Author: Krzysztof Burdzy
Journal: Trans. Amer. Math. Soc. 295 (1986), 35-57
MSC: Primary 60J65; Secondary 60G17
MathSciNet review: 831187
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Abstract: A skew-product decomposition of the $ n$-dimensional $ (n \geq 2)$ Brownian excursion law from a hyperplane is obtained. This is related to a Kolmogorov-type test for excursions from hyperplanes. Several results concerning existence, uniqueness and form of Brownian excursion laws from sufficiently "flat" surfaces are given. Some of these theorems are potential-theoretic in spirit. An extension of the results concerning excursion laws to an exit system in a Lipschitz domain is supplied.

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Keywords: Brownian excursions, excursion law, exit system, $ h$-process, Martin boundary, Lipschitz domain
Article copyright: © Copyright 1986 American Mathematical Society