The local time of iterated Brownian motion
type: Item
instance of: scholarly article
title: The local time of iterated Brownian motion
zbMATH Open document ID: 0857.60081
DOI: 10.1007/BF02214084
author: Endre Csáki
author: Miklós Csörgo
author: Antónia Földes
author: Pál Révész
published in: Journal of Theoretical Probability
publication date: 1996-10-13T00:00:00Z
review text: The study of the iterated Brownian motion \(H=\{H(t): = W_1(|W_2(t) |)\), \(t\geq 0\}\), where \(W_1\) and \(W_2\) are two independent Wiener processes, has motivated numerous works in the recent years. The purpose of the paper is to investigate the local time processes \(L^* = \{L^*(x,t), x\in {\mathbf R}\) and \(t \geq 0\}\) of \(H\), which is formally defined as \(L^*(x,t) = \int^t_0 \delta_x (H(s))ds\), where \(\delta_x\) stands for the Dirac point mass at \(x\). The authors establish a strong approximation result for \(L^*(x,t)\) in terms of the number of visits of a given site by an iterated (simple symmetric) random walk. Further results on the regularity of the local time process are proven, including the so-called upper-upper, upper-lower, lower-upper and lower-lower classes.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 934236
zbMATH Keywords: iterated Brownian motion
zbMATH Keywords: Dirac point mass
zbMATH Keywords: random walk
reviewed by: Jean Bertoin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02214084
OpenAlex ID: W2088750654
description: scientific article; zbMATH DE number 934236