  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
