Series representation for operator semistable laws and domains of normal attraction
type: Item
instance of: scholarly article
title: Series representation for operator semistable laws and domains of normal attraction
zbMATH Open document ID: 0935.60007
DOI: 10.1007/BF02432344
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-04-25T00:00:00Z
review text: This paper generalizes the so called Lepage series representation to operator semistable laws. A random vector \(Y\) with an operator semistable distribution \(\mu\) having no normal component is represented as an almost surely converging series of a function of simple random variables. These simple random variables are \(\Gamma\)-distributed random variables and random elements of the unit sphere obtained from the desintegration formula of the Lévy measure of \(\mu\). Furthermore the generalized domain of normal attraction of an operator semistable law having no normal component is characterized in terms of the convergence of order statistics relative to some polar-coordinate system obtained from an exponent of \(\mu\).
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1289192
zbMATH Keywords: operator semistable laws
zbMATH Keywords: Lepage series representation
zbMATH Keywords: order statistics
author: Hans-Peter Scheffler
reviewed by: Hans-Peter Scheffler
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02432344
OpenAlex ID: W2033225567
description: scientific article; zbMATH DE number 1289192