An almost sure invariance principle for the range of random walks
type: Item
instance of: scholarly article
title: An almost sure invariance principle for the range of random walks
zbMATH Open document ID: 0934.60044
DOI: 10.1016/S0304-4149(98)00053-2
author: Yuji Hamana
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: The author investigates invariance principles for the range of a random walk moving on the four or more dimensional integer lattice and starting from the origin. The range of random walks, \(R_n\), is considered as the number of distinct lattice sites visited at least once by the random walk in the first \(n\) steps. It is proved that the centralized and linearly interpolated range of the random walk can be asymptotically equal to a Brownian motion almost surely.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1364517
zbMATH Keywords: almost sure invariance principle
zbMATH Keywords: range of random walks
zbMATH Keywords: Brownian motion
reviewed by: Ivan Křivý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364517