1. The Malliavin-Stein method for Hawkes functionals.
- Author
-
Hillairet, Caroline, Huang, Lorick, Khabou, Mahmoud, and Réveillac, Anthony
- Subjects
MALLIAVIN calculus ,MATHEMATICAL bounds ,RANDOM variables ,CENTRAL limit theorem ,GAUSSIAN measures - 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 the law of functionals of a compound Hawkes process and the one of a Gaussian random variable. To achieve this, we rely on the Poisson imbedding representation of a 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 a quantitative Central Limit Theorem for the compound Hawkes process. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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