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On the simulation of general multivariate gamma distributions using Dickman approximations

Author

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  • Michael Grabchak

    (University of North Carolina Charlotte)

  • Xingnan Zhang

    (University of North Carolina Charlotte)

Abstract

We derive a Dickman approximation for the small jumps of a large class of multivariate Lévy processes. We then apply this approximation to develop a simulation method for the class of general multivariate gamma distributions (GMGD). A small-scale simulation study suggests that this method works very well.

Suggested Citation

  • Michael Grabchak & Xingnan Zhang, 2026. "On the simulation of general multivariate gamma distributions using Dickman approximations," Computational Statistics, Springer, vol. 41(3), pages 1-25, April.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:3:d:10.1007_s00180-026-01725-7
    DOI: 10.1007/s00180-026-01725-7
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    References listed on IDEAS

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    1. Michael Grabchak, 2025. "On the Self-Similarity of Remainder Processes and the Relationship Between Stable and Dickman Distributions," Mathematics, MDPI, vol. 13(6), pages 1-15, March.
    2. Barczy, Mátyás & Pap, Gyula, 2006. "Portmanteau theorem for unbounded measures," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1831-1835, November.
    3. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.
    4. Michael Grabchak, 2015. "Inversions of Lévy Measures and the Relation Between Long and Short Time Behavior of Lévy Processes," Journal of Theoretical Probability, Springer, vol. 28(1), pages 184-197, March.
    5. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    6. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma-Related OU Processes: Application to the Pricing of Energy Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(3), pages 207-227, May.
    7. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    8. Michael Grabchak, 2017. "A simple condition for the multivariate CLT and the attraction to the Gaussian of Lévy processes at long and short times," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 446-456, January.
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