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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. 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.
    2. 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.
    3. Masmoudi, Afif & Rejeb, Hajer, 2023. "Infinitely divisible matrix gamma distribution: Asymptotic behaviour and parameters estimation," Statistics & Probability Letters, Elsevier, vol. 194(C).
    4. 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).
    5. 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.
    6. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    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, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, December.
    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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