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Multivariate subexponential distributions

Author

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  • Cline, Daren B. H.
  • Resnick, Sidney I.

Abstract

We present a formulation of subexponential and exponential tail behavior for multivariate distributions. The definitions are necessarily in terms of vague convergence of Radon measures rather than of ratios of distribution tails. With the proper setting, we show that if all one dimensional marginals of a d-dimensional distribution are subexponential, then the distribution is multivariate subexponential. Known results for univariate subexponential distributions are extended to the multivariate setting. Point process arguments are used for the proofs.

Suggested Citation

  • Cline, Daren B. H. & Resnick, Sidney I., 1992. "Multivariate subexponential distributions," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 49-72, August.
    • Handle: RePEc:eee:spapps:v:42:y:1992:i:1:p:49-72
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    Cited by:

    1. Omey, Edward & Vesilo, R., 2009. "Random Sums of Random Variables and Vectors," Working Papers 2009/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Anita Behme & Philipp Lukas Strietzel, 2021. "A $$2~{\times }~2$$ 2 × 2 random switching model and its dual risk model," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 27-64, October.
    3. Miriam Hägele & Jaakko Lehtomaa, 2023. "On the Identification of the Riskiest Directional Components from Multivariate Heavy-Tailed Data," Risks, MDPI, vol. 11(7), pages 1-18, July.
    4. Hägele, Miriam, 2020. "Precise asymptotics of ruin probabilities for a class of multivariate heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 166(C).
    5. Miriam Hägele & Jaakko Lehtomaa, 2021. "Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance," JRFM, MDPI, vol. 14(5), pages 1-18, May.
    6. Weng, Chengguo & Zhang, Yi, 2012. "Characterization of multivariate heavy-tailed distribution families via copula," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 178-186.

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