An integral test for the supremum of Wiener local time
type: Item
instance of: scholarly article
title: An integral test for the supremum of Wiener local time
zbMATH Open document ID: 0677.60087
DOI: 10.1007/BF00333148
publication date: 1989-01-01T00:00:00Z
review text: Let L(x,t) (x\(\in {\mathbb{R}}\), \(t\geq 0)\), be the jointly continuous Brownian local time, and introduce \(L^*(t)=\sup_{x\in {\mathbb{R}}}L(x,t)\). A positive nondecreasing function a belongs to the upper-upper class (respectively the upper-lower class) of \(L^*\) if \(L^*(t)\leq a(t)\) for all large enough t a.s. (respectively if for a.e. \(\omega\), there is a sequence \(t_ i=t_ i(\omega)\), lim \(t_ i=\infty\), such that, for every integer i, \(L^*(t_ i)>a(t))\). These classes are characterized by an integral test.
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 4109794
zbMATH Keywords: supremum of Wiener local time
zbMATH Keywords: Brownian local time
zbMATH Keywords: upper-upper class
zbMATH Keywords: integral test
author: Endre Csáki
reviewed by: Jean Bertoin
MaRDI profile type: Publication
cites work: Q4765078
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full work available at URL: https://doi.org/10.1007/bf00333148
OpenAlex ID: W1548722570
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4109794