Mesure du voisinage and occupation density
type: Item
instance of: scholarly article
title: Mesure du voisinage and occupation density
zbMATH Open document ID: 0581.60059
DOI: 10.1007/BF00339937
author: Pál Révész
author: Miklós Csörgo
publication date: 1986-01-01T00:00:00Z
review text: Let W(t) be a standard Wiener process with occupation density (local time) \(\eta\) (x,t). P. Lévy showed that for each x, \(\eta\) (x,t) is a.s. equal to the ''mesure du voisinage'' of W, i.e., to the limit as h approaches zero of \(h^{1/2}\) times N(h,x,t), the number of excursions from x, exceeding h in length, that are completed by W up to time t. Recently E. Perkins showed that the exceptional null sets, which may depend on x, can be combined into a single null set off which the above convergence is uniform in x. The main aim of the present paper is to estimate the rate of convergence in Perkins' theorem as h goes to zero. We also investigate the connection between N and \(\eta\) in the case when we observe a Wiener process through a long time t and consider the number of long (but much shorter than t) excursions.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 3930067
zbMATH Keywords: mesure du voisinage
zbMATH Keywords: occupation density
zbMATH Keywords: rate of convergence
MaRDI profile type: Publication
cites work: Q5332526
cites work: Brownian Local Times and Taboo Processes
cites work: Q3908217
cites work: A global intrinsic characterization of Brownian local time
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 3930067