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

Nikolai Leonenko; Claudio Macci; Barbara Pacchiarotti

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arXiv · 2004.09315

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

Nikolai Leonenko·Claudio Macci·Barbara Pacchiarotti

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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.

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Nikolai Leonenko, Claudio Macci, Barbara Pacchiarotti. 2020-04-20. Large deviations for a class of tempered subordinators and their inverse processes. https://arxiv.org/abs/2004.09315

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