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Infinitely divisible multivariate and matrix Gamma distributions

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  • Pérez-Abreu, Victor
  • Stelzer, Robert

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.

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  • Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:155-175
    DOI: 10.1016/j.jmva.2014.04.017
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    References listed on IDEAS

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    Cited by:

    1. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    2. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    3. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    4. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    5. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, June.
    6. Masmoudi, Afif & Rejeb, Hajer, 2023. "Infinitely divisible matrix gamma distribution: Asymptotic behaviour and parameters estimation," Statistics & Probability Letters, Elsevier, vol. 194(C).
    7. Kozubowski, Tomasz J. & Mazur, Stepan & Podgórski, Krzysztof, 2022. "Matrix Gamma Distributions and Related Stochastic Processes," Working Papers 2022:12, Örebro University, School of Business.
    8. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    9. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.

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