Asymptotic results for families of random variables having power series distributions
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator
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. The notion of noncentral moderate deviations is used when the weak convergence is towards a non-Gaussian distribution. In this paper, noncentral moderate deviation results are presented for two fractional Skellam processes known in the literature (see [20]). It is established that, for the fractional Skellam process of type 2 (for which one can refer to the recent results for compound fractional Poisson processes in [3]), the convergences to zero are usually faster because one can prove suitable inequalities between rate functions.
On count data models based on Bernstein functions or their inverses
Giuseppe D'Onofrio, Federico Polito, Živorad Tomovski