Some examples of noncentral moderate deviations for sequences of real random variables

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. In this paper, some examples of classes of large deviation principles of this kind are presented, but the involved random variables converge weakly to Gumbel, exponential and Laplace distributions.

Noncentral moderate deviations for fractional Skellam processes

“…The term noncentral moderate deviations has been recently used in the literature when we have a class of large deviation principles that, in some sense, fills the gap between a convergence to a constant (typically zero) and the weak convergence towards a non-Gaussian distribution. Some examples of noncentral moderate deviations can be found in [12], where the weak convergences are towards Gumbel, exponential, and Laplace distributions. In that reference, the interested reader can find some other previous references in the literature with some other examples.…”