Infinitely divisible multivariate and matrix Gamma distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:130

Article

Perez-Abreu, Victor¹  Stelzer, Robert² 

[1] Ctr Res Math CIMAT, Dept Probabil & Stat, Guanajuato, Mexico

[2] Univ Ulm, Inst Math Finance, D-89069 Ulm, Germany

关键词: Infinite divisibility;    Random matrix;    Cone valued distribution;    Levy process;    Matrix subordinator;   

DOI  :  10.1016/j.jmva.2014.04.017

来源: Elsevier

【 摘 要 】

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 Ito-Wiener integral with respect to an infinitely divisible random measure associated to the jumps of a Levy process is established. A new example of an infinitely divisible positive definite Gamma random matrix is introduced. It has properties which make it appealing for modelling under an infinite divisibility framework. An interesting relation of the moments of the Levy measure and the Wishart distribution is highlighted which we suppose to be important when considering the limiting distribution of the eigenvalues. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free