Sub-fractional Brownian motion and its relation to occupation times
type: Item
instance of: scholarly article
title: Sub-fractional Brownian motion and its relation to occupation times
zbMATH Open document ID: 1076.60027
author: Tomasz Bojdecki
author: Anna Talarczyk
author: Luis G. Gorostiza
published in: Statistics \& Probability Letters
publication date: 2005-04-21T00:00:00Z
review text: The authors study a class of centered Gaussian processes on \([0,\infty)\) which they call ``sub-fractional Brownian motions''. The covariance function is given by \[ s^h + t^h -\tfrac{1}{2}\left[ (s+t)^h +| s-t| ^h\right]\;,\quad t,s\geq 0\;, \] for a certain \(h\in (0,2)\). Of course, if \(h=1\), one gets the ordinary Brownian motion. Properties of those processes are stated and proved, for example, self-similarity and path properties. Finally, it is shown how those processes arise in the investigation of occupation time fluctuations of some certain particle systems.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 2160034
zbMATH Keywords: long-range dependence
MaRDI profile type: Publication
full work available at URL: j.spl.2004.06.035
OpenAlex ID: W2152838163
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DOI: 10.1016/J.SPL.2004.06.035
description: scientific article; zbMATH DE number 2160034