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Large deviations for a class of tempered subordinators and their inverse processes

Part of: Markov processes Stochastic processes Limit theorems

Published online by Cambridge University Press:  08 January 2021

Nikolai Leonenko ,
Claudio Macci  and
Barbara Pacchiarotti
Nikolai Leonenko
Affiliation:
Cardiff School of Mathematics, Cardiff University, Senghennydd Road Cardiff, CF24 4AG, UK (leonenkon@cardiff.ac.uk)
Claudio Macci
Affiliation:
Cardiff School of Mathematics, Cardiff University, Senghennydd Road Cardiff, CF24 4AG, UK (leonenkon@cardiff.ac.uk)
Barbara Pacchiarotti
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica I-00133 Rome, Italy (macci@mat.uniroma2.it; pacchiar@mat.uniroma2.it)
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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.

Keywords

Mittag–Leffler functionnon-central moderate deviationsrandom time-changesTweedie distribution

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G52: Stable processes 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 2030 - 2050
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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