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The Malliavin-Stein method for Hawkes functionals

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-Esséen bounds associated to Central Limit Theorems for the compound Hawkes process.
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Preprints, Working Papers, ...
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Contributor : Anthony Reveillac <>
Submitted on : Sunday, April 4, 2021 - 12:41:05 PM
Last modification on : Friday, April 9, 2021 - 3:21:27 AM


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  • HAL Id : hal-03189614, version 1


Caroline Hillairet, Lorick Huang, Mahmoud Khabou, Anthony Réveillac. The Malliavin-Stein method for Hawkes functionals. 2021. ⟨hal-03189614⟩



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