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Large deviations for fractional Poisson processes

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  • Beghin, Luisa
  • Macci, Claudio

Abstract

We prove large deviation principles for two versions of fractional Poisson processes: the main version is a renewal process, the alternative version is a weighted Poisson process. We also present asymptotic results for the ruin probabilities of an insurance model with a fractional Poisson claim number process.

Suggested Citation

  • Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1193-1202
    DOI: 10.1016/j.spl.2013.01.017
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    References listed on IDEAS

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    1. Joan Del Castillo & Marta Pérez-Casany, 1998. "Weighted Poisson Distributions for Overdispersion and Underdispersion Situations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 567-585, September.
    2. Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
    3. Mauro Politi & Taisei Kaizoji & Enrico Scalas, 2011. "Full characterization of the fractional Poisson process," Papers 1104.4234, arXiv.org.
    4. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
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    Cited by:

    1. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    2. Kreer, Markus & Kızılersü, Ayşe & Thomas, Anthony W., 2014. "Fractional Poisson processes and their representation by infinite systems of ordinary differential equations," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 27-32.
    3. repec:eee:stapro:v:129:y:2017:i:c:p:260-268 is not listed on IDEAS

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