Lévy's Brownian motion as a set-indexed process and a related central limit theorem
type: Item
instance of: scholarly article
title: Lévy's Brownian motion as a set-indexed process and a related central limit theorem
zbMATH Open document ID: 0585.60008
DOI: 10.1016/0304-4149(85)90382-5
author: Mina Ossiander
author: Ronald Pyke
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: A representation of Lévy's Brownian motion with multi-dimensional time is given as a set-indexed process with independent increments. This construction yields a unified approach of Lévy's Brownian motion and the Brownian sheet, where a particular family of spheres plays the same basic role for Lévy's Brownian motion as the family of rectangles plays for the Brownian sheet. Some related limit theorems are proved for a natural family of set-indexed empirical processes.
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 3938123
zbMATH Keywords: Brownian motion with multi-dimensional time
zbMATH Keywords: set-indexed process with independent increments
zbMATH Keywords: Brownian sheet
zbMATH Keywords: empirical processes
reviewed by: J.-F. Le Gall
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90382-5
OpenAlex ID: W2034031353
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description: scientific article; zbMATH DE number 3938123