2021/04/04 by Caroline Hillairet, Hillairet, Caroline, Lorick Huang +5 · 2 citations
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · doi:10.48550/arxiv.2104.01583
openalex publication_date 2021/04/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.