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Asymptotic analysis of Poisson shot noise processes, and applications

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  • Torrisi, Giovanni Luca
  • Leonardi, Emilio

Abstract

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

Suggested Citation

  • Torrisi, Giovanni Luca & Leonardi, Emilio, 2022. "Asymptotic analysis of Poisson shot noise processes, and applications," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 229-270.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:229-270
    DOI: 10.1016/j.spa.2021.11.008
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    References listed on IDEAS

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    1. Stabile, Gabriele & Torrisi, Giovanni Luca, 2010. "Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1200-1209, August.
    2. Torrisi, G. L., 2004. "Simulating the ruin probability of risk processes with delay in claim settlement," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 225-244, August.
    3. Macci, Claudio & Torrisi, Giovanni Luca, 2004. "Asymptotic results for perturbed risk processes with delayed claims," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 307-320, April.
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    Cited by:

    1. Kirchner, Matthias & Torrisi, Giovanni Luca, 2023. "Fluctuations and precise deviations of cumulative INAR time series," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 1-32.

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