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Ratios of ordered points of point processes with regularly varying intensity measures

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  • Ipsen, Yuguang
  • Maller, Ross
  • Resnick, Sidney

Abstract

We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to “large-trimming” properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson–Dirichlet distribution.

Suggested Citation

  • Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2019. "Ratios of ordered points of point processes with regularly varying intensity measures," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 205-222.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:1:p:205-222
    DOI: 10.1016/j.spa.2018.02.015
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    References listed on IDEAS

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    1. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.
    2. Smid, B. & Stam, A. J., 1975. "Convergence in distribution of quotients of order statistics," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 287-292, July.
    3. Gregoire, Gérard, 1984. "Negative binomial distributions for point processes," Stochastic Processes and their Applications, Elsevier, vol. 16(2), pages 179-188, February.
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    Cited by:

    1. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2020. "Trimmed Lévy processes and their extremal components," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2228-2249.

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