Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion
type: Item
instance of: scholarly article
title: Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion
zbMATH Open document ID: 1179.60051
DOI: 10.1214/08-AIHP173
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2009-08-24T00:00:00Z
full work available at URL: https://eudml.org/doc/78032
review text: Let \(\xi(k,n)\), \(n\geq 1\), \(k\in \mathbb{Z}\), be a local time of a symmetric simple random walk on a line, or, in other words, a number of excursions away from \(k\) completed before \(n\). The paper is devoted to the strong approximations of centered local time \(\xi(k,n)-\xi(0,n)\) in terms of a Brownian sheet and an independent Wiener process, time changed by an independent Brownian local time. Some consequences such as week convergence and the laws of iterated logarithm (related to \(\xi(k,n)\)) are established. The paper also contains a survey and an extensive list of references concerning the results on such strong approximations of the local time.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 5598059
zbMATH Keywords: local time
zbMATH Keywords: random walk
zbMATH Keywords: Brownian sheet
zbMATH Keywords: strong approximation
author: Endre Csáki
author: Miklós Csörgo
author: Antónia Földes
author: Pál Révész
reviewed by: V. Knopova
MaRDI profile type: Publication
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OpenAlex ID: W2034032960
description: scientific article; zbMATH DE number 5598059