The Malliavin-Stein method for Hawkes functionals
Probability
2021-04-06 v1
Abstract
In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between functionals of a compound Hawkes process and a given Gaussian density. To achieve this, we rely on the Poisson embedding representation of an Hawkes process to provide a Malliavin calculus for the Hawkes processes, and more generally for compound Hawkes processes. As an application, we close a gap in the literature by providing the first Berry-Ess\'een bounds associated to Central Limit Theorems for the compound Hawkes process.
Keywords
Cite
@article{arxiv.2104.01583,
title = {The Malliavin-Stein method for Hawkes functionals},
author = {Caroline Hillairet and Lorick Huang and Mahmoud Khabou and Anthony Reveillac},
journal= {arXiv preprint arXiv:2104.01583},
year = {2021}
}