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 
Luisa Beghin and Claudio Macci
math.PR