Type \(G\) distributions on \({\mathbb R}^d\)
type: Item
instance of: scholarly article
title: Type \(G\) distributions on \({\mathbb R}^d\)
zbMATH Open document ID: 1023.60023
DOI: 10.1023/A:1015044726122
author: M. Maejima
author: Jan Rosiński
published in: Journal of Theoretical Probability
publication date: 2002-08-20T00:00:00Z
review text: The authors present a systematic study of the class of multivariate distributions obtained by a Gaussian randomization of jumps of a Lévy process. It is shown that this class of distributions, called type \(G\) distributions, is a closed convolution semigroup of the set of symmetric infinitely divisible measures with respect to weak convergence. The Lévy measure of a type \(G\) distribution is characterized in terms of a polar decomposition and so called type \(G\) processes are introduced as those with type \(G\) finite-dimensional marginals. The authors construct an infinitely divisible distribution which is not of type \(G\), but all lower dimensional projections, especially the one-dimensional marginals, are of type \(G\). Moreover, a series representation of type \(G\) random vectors is presented.
reviewed by: Hans-Peter Scheffler
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60G52
zbMATH DE Number: 1784211
zbMATH Keywords: type \(G\) distributions
zbMATH Keywords: series representation
zbMATH Keywords: Lévy representation
zbMATH Keywords: variance mixture of normal distribution
MaRDI profile type: Publication
full work available at URL: a:1015044726122
OpenAlex ID: W2911812073
description: scientific article; zbMATH DE number 1784211