Large deviations for a class of tempered subordinators and their inverse processes
Abstract
We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate deviations result. More precisely we mean a class of large deviation principles that fill the gap between the (trivial) weak convergence of some non-Gaussian identically distributed random variables to their common law, and the convergence of some other related random variables to a constant. Some other minor results concern large deviations for the inverse of the tempered subordinators considered in this paper; actually, in some results, these inverse processes appear as random time-changes of other independent processes.
Cite
@article{arxiv.2004.09315,
title = {Large deviations for a class of tempered subordinators and their inverse processes},
author = {Nikolai Leonenko and Claudio Macci and Barbara Pacchiarotti},
journal= {arXiv preprint arXiv:2004.09315},
year = {2020}
}