Random self-decomposability and autoregressive processes
type: Item
instance of: scholarly article
title: Random self-decomposability and autoregressive processes
zbMATH Open document ID: 1213.60035
author: Tomasz J. Kozubowski
author: Krzysztof Podgórski
published in: Statistics \& Probability Letters
publication date: 2010-09-24T00:00:00Z
review text: The authors introduce the random self-decomposability. We say that a distribution with the characteristic function \(\psi\) is random self-decomposable if for each \(p\in[0,1]\) and \(c\in[0,1]\) there exists a probability distribution with the characteristic function \(\psi_{c,p}\) such that \(\psi(t)=\psi_{c,p}(t)(p+(1-p)\psi(ct))\). The authors show that \({\mathcal C}_{RSD}={\mathcal C}_{SD}\cap {\mathcal C}_{GID}\), where \({\mathcal C}_{RSD}\), \({\mathcal C}_{SD}\) and \({\mathcal C}_{GID}\) are the classes of random self-decomposable, self-decomposable and geometrically infinitely divisible distributions, respectively. Also, they provide the connections between the random self-decomposability and AR structures.
reviewed by: Miroslav M. Ristić
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 5791190
zbMATH Keywords: geometric infinite divisibility
zbMATH Keywords: geometric stable law
zbMATH Keywords: Laplace distribution
zbMATH Keywords: Linnik distribution
zbMATH Keywords: non-Gaussian time series
MaRDI profile type: Publication
full work available at URL: j.spl.2010.06.014
OpenAlex ID: W2136907510
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DOI: 10.1016/J.SPL.2010.06.014
description: scientific article; zbMATH DE number 5791190