Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\)
type: Item
instance of: scholarly article
title: Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\)
zbMATH Open document ID: 0628.60009
DOI: 10.1007/BF00334208
author: Zbigniew J. Jurek
publication date: 1988-01-01T00:00:00Z
review text: For a bounded linear operator Q, on a Banach space E, and a real number \(\beta\), there are introduced classes, \({\mathcal U}_{\beta}(Q)\), of some limit distributions such that \({\mathcal U}_ 0(I)\) coincides with the Lévy class \(L_ 0\). Elements from \({\mathcal U}_{\beta}(Q)\) are characterized in terms of convolution equations and as probability distributions of some random integral functionals. The continuity and fixed points of this random mapping are studied. It is shown that fixed points coincide with the class of Q-stable measures.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 4022239
zbMATH Keywords: convolution equations
zbMATH Keywords: random integral functionals
zbMATH Keywords: Lévy class
zbMATH Keywords: infinitely divisible measures
zbMATH Keywords: Skorohod topology
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00334208
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4022239