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arXiv · 2104.01583

The Malliavin-Stein method for Hawkes functionals

Caroline Hillairet·Lorick Huang·Mahmoud Khabou·Anthony Reveillac
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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.

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BibTeXRIS

Caroline Hillairet, Lorick Huang, Mahmoud Khabou, Anthony Reveillac. 2021-04-04. The Malliavin-Stein method for Hawkes functionals. https://arxiv.org/abs/2104.01583

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