The symmetry group and exponents of operator stable probability measures
type: Item
instance of: scholarly article
title: The symmetry group and exponents of operator stable probability measures
zbMATH Open document ID: 0603.60011
author: William N. Hudson
author: Zbigniew J. Jurek
author: Jerry Alan Veeh
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Let \(\mu\) be an operator-stable probability measure on a finite- dimensional real vector space \({\mathcal V}\). The role of the index in the one-dimensional case is played by an invertible linear operator \({\mathcal B}\) on \({\mathcal V}\) called the exponent of \(\mu\). There exist exponents of \(\mu\) which commute with every operator in the measure's symmetry group. This result is used to find the representation of the Levy measure of \(\mu\) which does not depend on the choice of an exponent.
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 3973940
zbMATH Keywords: operator-stable probability measure
zbMATH Keywords: Levy measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992455
OpenAlex ID: W1996447901
DOI: 10.1214/AOP/1176992455
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description: scientific article; zbMATH DE number 3973940