Normal approximation of Functionals of Point Processes: Application to Hawkes Processes.
Abstract
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 imbedding 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.
Fields of Study & Subjects
Point processes and geometric inequalities
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–44
- Publication date
- 1 January 2026
- Language
- EN