Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.insa-toulouse.fr/hal-03189614
Contributor : Anthony Reveillac <>
Submitted on : Sunday, April 4, 2021 - 12:41:05 PM
Last modification on : Friday, April 9, 2021 - 3:21:27 AM

File

Hillairet_Huang_Khabou_Reveill...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03189614, version 1

Citation

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

Share

Metrics

Record views

12

Files downloads

11