Noncentral moderate deviations for time-changed multivariate Lévy processes with linear combinations of inverse stable subordinators

¹ Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India
² Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 December 2024
Accepted: 14 May 2025

Abstract

The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation principle) and a weak convergence to a non- Gaussian (and non-degenerating) distribution. Some noncentral moderate deviation results in the literature concern time-changed univariate Lévy processes, where the time-changes are given by inverse stable subordinators. In this paper we present analogue results for multivariate Lévy processes; in particular the random time-changes are suitable linear combinations of independent inverse stable subordinators.