Non-central moderate deviations for compound fractional Poisson processes

2021/09/16 by Luisa Beghin, Beghin, Luisa, Claudio Macci +1
Economics, Econometrics and Finance · Mathematics · #33E12 #60F05 #60F10 #60G22 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2109.07862

openalex publication_date 2021/09/16 · openalex created_date 2022/07/24 · openalex updated_date 2026/08/01

Abstract

The term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about "non-central moderate deviations" when the weak convergence is towards a non-Gaussian distribution. In this paper we study non-central moderate deviations for compound fractional Poisson processes with light-tailed jumps.

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