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Large deviations for fractional Poisson processes

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  • Beghin, Luisa
  • Macci, Claudio
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 4 ()
    Pages: 1193-1202

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1193-1202

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    Related research

    Keywords: Mittag-Leffler function; Renewal process; Ruin probability; Weighted Poisson distribution; Relative entropy;

    References

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

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