Noncentral moderate deviations for fractional Skellam processes
Volume 11, Issue 1 (2024), pp. 43–61
Pub. online: 5 December 2023
Type: Research Article
Open Access
Open Access
Received
29 July 2023
29 July 2023
Revised
3 November 2023
3 November 2023
Accepted
3 November 2023
3 November 2023
Published
5 December 2023
5 December 2023
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. 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.
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