4 papers
Quantification of limit theorems for Hawkes processes
Laure Coutin, Benjamin Massat, Anthony Réveillac
In this article, we fill a gap in the literature regarding quantitative functional central limit theorems (qfCLT) for Hawkes processes by providing an upper bound for the convergen…
Normal approximation of Functionals of Point Processes: Application to Hawkes Processes
Laure Coutin, Benjamin Massat, Anthony Réveillac
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 conjuncti…
Multivariate Self-Exciting Processes with Dependencies
Caroline Hillairet, Thomas Peyrat, Anthony Réveillac
This paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, in…
Poisson imbedding meets the Clark-Ocone formula
Caroline Hillairet, Thomas Peyrat, Anthony Réveillac
In this paper we develop a representation formula of Clark-Ocone type for any integrable Poisson functionals, which extends the Poisson imbedding for point processes. This represen…