Large deviations for fractional Poisson processes
Copyright policy )Large deviations for fractional Poisson processes
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
- Roma Tre University Italy
- Sapienza University of Rome Italy
- University of Rome Tor Vergata Italy
Mittag-Leffler function, Relative entropy, renewal process, Ruin probability, relative entropy, Probability (math.PR), Fractional processes, including fractional Brownian motion, Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA, renewal process; ruin probability; weighted poisson distribution; mittag-leffler function; relative entropy, Weighted Poisson distribution, Mittag-Leffler function; Renewal process; Ruin probability; Weighted Poisson distribution; Relative entropy, Large deviations, 60F10, 33E12, 60G22, 60K05, 91B30, weighted Poisson distribution, Risk theory, insurance, Renewal proce, FOS: Mathematics, ruin probability, Mathematics - Probability
Mittag-Leffler function, Relative entropy, renewal process, Ruin probability, relative entropy, Probability (math.PR), Fractional processes, including fractional Brownian motion, Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA, renewal process; ruin probability; weighted poisson distribution; mittag-leffler function; relative entropy, Weighted Poisson distribution, Mittag-Leffler function; Renewal process; Ruin probability; Weighted Poisson distribution; Relative entropy, Large deviations, 60F10, 33E12, 60G22, 60K05, 91B30, weighted Poisson distribution, Risk theory, insurance, Renewal proce, FOS: Mathematics, ruin probability, Mathematics - Probability
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