On the character of convergence to Brownian local time. II
type: Item
instance of: scholarly article
title: On the character of convergence to Brownian local time. II
zbMATH Open document ID: 0572.60079
DOI: 10.1007/BF00699106
author: A. N. Borodin
publication date: 1986-01-01T00:00:00Z
review text: [For part I see the foregoing review, Zbl 0572.60078.] In this paper we consider the sequences of stochastic processes which converge weakly as \(n\to \infty\) to Brownian local time. These processes are generated by a recurrent random walk with finite variance. The main result is the following: It is possible to redefine a random walk in such a way that for a wide class of processes the normalized differences between them and Brownian local time converge in distribution to some stochastic process. We also prove that such differences with probability one have the logarithmic upper bound. It is the so called ''strong invariance principles for local times''.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 3913403
zbMATH Keywords: Brownian local time
zbMATH Keywords: strong invariance principles for local times
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00699106
OpenAlex ID: W4253157143
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 3913403