Gaussian approximation and moderate deviations of poisson shot noises with application to compound generalized Hawkes processes
Author(s)
Khabou, M
Torrisi, GL
Type
Journal Article
Abstract
In this article, we give explicit bounds on the Wasserstein and the Kolmogorov distances between random variables lying in the first chaos of the Poisson space and the standard Normal distribution, using the results proved in [30]. Relying on the theory developed in [40] and on a fine control of the cumulants of the first chaoses, we also derive moderate deviation principles, Bernstein-type concentration inequalities and Normal approximation bounds with Cram´er correction terms for the same variables. The aforementioned results are then applied to Poisson shot-noise processes and, in particular, to the generalized compound Hawkes point processes (a class of stochastic models, introduced in this paper, which generalizes classical Hawkes processes). This extends the recent results in [23, 26] regarding the Normal approximation and in [47] for moderate deviations.
Date Acceptance
2024-06-04
ISSN
0001-8678
Publisher
Applied Probability Trust
Journal / Book Title
Advances in Applied Probability
Copyright Statement
This paper is embargoed until publication.
Publication Status
Accepted
Rights Embargo Date
10000-01-01