Operator self-similar processes on Banach spaces
type: Item
instance of: scholarly article
title: Operator self-similar processes on Banach spaces
zbMATH Open document ID: 1116.60014
DOI: 10.1155/JAMSA/2006/82838
author: Mihaela T. Matache
author: V. Matache
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/53250
review text: The authors investigate operator self-similar processes (OSS) on a Banach space \(E\) using the theory of one-parameter groups of operators on \(E\). One of the main results claims that if \(\{ X(t) : t>0 \}\) is OSS and if \(\text{Span}(EX(t) : t>0) = E\), then its scaling family of operators is a uniquely determined multiplicative group. Moreover, if \(EX(t)\) is continuous and \(\text{Span}(EX(t): t>0)\) is a subset having category 2 (in the sense of Baire), then \(EX(t)\) has a power-growth with exponent \(a\geq 0\).
reviewed by: Elisaveta Pancheva
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 5134593
zbMATH Keywords: self-similar processes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5134593