A representation of local time for Lipschitz surfaces
type: Item
instance of: scholarly article
title: A representation of local time for Lipschitz surfaces
zbMATH Open document ID: 0669.60074
DOI: 10.1007/BF01198318
author: Rodrigo Bañuelos
author: Richard F. Bass
author: K. Burdzy
publication date: 1990-01-01T00:00:00Z
review text: Suppose that \(D\subset {\mathbb{R}}^ n\), \(n\geq 2\), is a Lipschitz domain and let \(N_ t(r)\) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then \(rN_ t(r)\) converges as \(r\to 0\) to a constant multiple of local time on \(\partial D\), a.s. and in \(L^ p\) for all \(p<\infty\). The limit need not exist or may be trivial (0 or \(\infty)\) in Hölder domains, non- tangentially accessible domains and domains whose boundaries have finite surface area.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4096530
zbMATH Keywords: number of excursions of Brownian motion
zbMATH Keywords: local time
zbMATH Keywords: Hölder domains
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4096530