Large deviations for fractional Poisson processes
AbstractWe 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 InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 83 (2013)
Issue (Month): 4 ()
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- Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
- Mauro Politi & Taisei Kaizoji & Enrico Scalas, 2011. "Full characterization of the fractional Poisson process," Papers 1104.4234, arXiv.org.
- Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
- 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.
- 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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