Non-central moderate deviations for compound fractional Poisson processes

Abstract

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about non-central moderate deviations when the weak convergence is towards a non-Gaussian distribution. In this paper we study non-central moderate deviations for compound fractional Poisson processes with light-tailed jumps.