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

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.