Infinitely divisible multivariate and matrix Gamma distributions

Victor Pérez-Abreu and Robert Stelzer

Journal of Multivariate Analysis, 2014, vol. 130, issue C, 155-175

Abstract: Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite matrices in applications. The cone-valued class of generalised Gamma convolutions is studied. In particular, a characterisation in terms of an Itô–Wiener integral with respect to an infinitely divisible random measure associated to the jumps of a Lévy process is established.

Keywords: Infinite divisibility; Random matrix; Cone valued distribution; Lévy process; Matrix subordinator (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.jmva.2014.04.017

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