Elliptical symmetry and characterization of operator-stable and operator semi-stable measures
type: Item
instance of: scholarly article
title: Elliptical symmetry and characterization of operator-stable and operator semi-stable measures
zbMATH Open document ID: 0549.60007
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: In this paper the author presents a characterization of an elliptically symmetric full-operator semi-stable measure on a finite dimensional real vector space V. As a corollary certain properties of full operator-stable measures are obtained. The paper concludes with a theorem giving necessary and sufficient conditions for a full infinitely divisible measure \(\mu\) on V to be (a) operator-stable or (b) strictly operator semi-stable, these conditions being framed in terms of the quasi- decomposability group of \(\mu\).
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 3876282
zbMATH Keywords: full-operator semi-stable measure
zbMATH Keywords: infinitely divisible measure
zbMATH Keywords: quasi- decomposability group
author: Andrzej Łuczak
reviewed by: Andrew Dale
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993151
OpenAlex ID: W1976923086
DOI: 10.1214/AOP/1176993151
Recommended article: Q4351662
Recommended article: The structure of the exponents and symmetries of an operator stable measure
Recommended article: Symmetry and nonuniformly elliptic operators.
Recommended article: Q4698012
Recommended article: A characterization of elliptic operators
Recommended article: Symmetrization of functions and principal eigenvalues of elliptic operators
Recommended article: Symmetries of Gaussian measures and operator colligations
Recommended article: Q3744707
description: scientific article; zbMATH DE number 3876282