Some vector-valued examples of noncentral moderate deviation results

2025/12/17 by Macci, Claudio, Pacchiarotti, Barbara
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probability and Risk Models #Financial Risk and Volatility Modeling #Random Matrices and Applications

paper · doi:10.48550/arxiv.2512.15527

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. Several examples can be found in the literature, mainly for real-valued random variables (see, e.g.,~\citeGiulianoMacci and the references cited therein). In this paper we present some examples with vector-valued random variables.

Citations

• Noncentral moderate deviations for time-changed multivariate Lévy processes with linear combinations of inverse stable subordinators
• Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators
• Some examples of non-central moderate deviations for sequences of real random variables
• Large deviations for a class of tempered subordinators and their inverse\n processes
• The Statistical Analysis of Compositional Data.

Related

• Some examples of non-central moderate deviations for sequences of real random variables
• Noncentral moderate deviations for time-changed multivariate Lévy processes with linear combinations of inverse stable subordinators
• Noncentral moderate deviations for fractional Skellam processes
• Linear response and moderate deviations: hierarchical approach. I
• Linear response and moderate deviations: hierarchical approach. IV