Large deviations for fractional Poisson processes

Luisa Beghin; Claudio Macci

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arXiv · 1204.1446

Large deviations for fractional Poisson processes

Luisa Beghin·Claudio Macci

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Abstract

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance model with constant premium rate, i.i.d. light tail claim sizes, and a fractional Poisson claim number process. We conclude with the alternative version where all the random variables are weighted Poisson distributed. Keywords: Mittag Leffler function; renewal process; random time cha

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Luisa Beghin, Claudio Macci. 2012-04-06. Large deviations for fractional Poisson processes. https://arxiv.org/abs/1204.1446

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