This article is cited in 14 papers

Extensions of type $G$ and marginal infinite divisibility

O. E. Barndorff-Nielsen^a, V. Pérez-Abreu<sup>b

a</sup> University of Aarhus
^b Center for Mathematical Research

Abstract: We say that a random variate on a Euclidean space is marginal infinitely divisible with respect to a class of linear mappings on that space if each of these mappings results in an infinitely divisible random variate. Special cases are applied in a multivariate extension of the concept of type $G$ probability laws. Random nonnegative matrices play a central role.

Keywords: inverse Wishart distribution, matrix inverse Gaussian law, multivariate normal inverse Gaussian law, multivariate stable laws, random positive definite matrices, self-decomposability.

Received: 08.06.2001

Language: English

DOI: 10.4213/tvp3649

 English version: Theory of Probability and its Applications, 2003, 47:2, 202–218

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