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Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions

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  • Stabile, Gabriele
  • Torrisi, Giovanni Luca

Abstract

In this note we provide a large deviation principle for Poisson shot noise processes under heavy tail semi-exponential conditions on the total shot per arrival. As in the light tail case, our result shows an insensitivity property of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1200-1209
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    References listed on IDEAS

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    1. 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.
    2. 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. Beghin, Luisa & Macci, Claudio, 2022. "Non-central moderate deviations for compound fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 185(C).
    2. Shen, Xinmei & Zhang, Yi, 2012. "Moderate deviations for a risk model based on the customer-arrival process," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 116-122.
    3. 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.

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