MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

MPS-RR 2000-27
July 2000

# Multivariate Type $\mathcal{G}$ Distributions

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## Abstract

The class of multivariate distributions all of whose one-dimensional projections are of type $G$ is discussed and examples of such distributions presented. In the course of this, we introduce a new representation of the cumulant function of the symmetric multivariate stable laws as well as multivariate extensions of the Inverse Gaussian and the symmetric Normal Inverse Gaussian laws. A concept of weak infinite divisibility of random matrices is introduced and this leads to further examples.

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This paper has now been published in Revised version has appeared in Theory Prob. Its Appl. 47 (2002), 202-218