On the increments of the local time of a Wiener sheet
type: Item
instance of: scholarly article
title: On the increments of the local time of a Wiener sheet
zbMATH Open document ID: 0581.60058
DOI: 10.1016/0047-259X(85)90021-1
author: Pál Révész
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: The Wiener sheet W can be viewed as a continuous random function defined on the quadrant [0,\(\infty)\times [0,\infty)\). The local time \(\eta\) (u,A) at level u is a (random) measure of the level set \(\{s\in A:W(s)=u\}\). Detailed estimates are used to obtain information about \(\eta\) (u,A) when A is small. For example: suppose K is a compact subset of the open quadrant (0,\(\infty)\times (0,\infty)\). Let S(h) be the supremum of \(\eta\) (u,Q) for all u and all boxes Q in K of area h or less. Then it follows rapidly from Theorem 3 that \(S(h)=o(h^{3/4}(\log h^{-1})^ 3)\) as \(h\to 0\), with probability one.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3930066
zbMATH Keywords: continuity modulus
zbMATH Keywords: occupation time
zbMATH Keywords: Wiener sheet
zbMATH Keywords: local time
reviewed by: Wilfrid S. Kendall
MaRDI profile type: Publication
cites work: Q3049621
cites work: How big are the increments of the local time of a Wiener process?
cites work: Q4170025
cites work: Q5822308
cites work: A lower lipschitz condition for the stable subordinator
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full work available at URL: 0047-259x(85)90021-1
OpenAlex ID: W2048445434
description: scientific article; zbMATH DE number 3930066