2024/07/29 by Laure Coutin, Coutin, Laure, Benjamin Massat +3
Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2407.19806
openalex publication_date 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding representation, our result applies to a variety of point processes including discrete and continuous Hawkes processes. In particular, we establish an explicit convergence rate for stable continuous non-linear Hawkes processes and for discrete Hawkes processes. Finally, we obtain an upper bound in the context of nearly unstable Hawkes processes.