The Malliavin-Stein method for Hawkes functionals

In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on Wasserstein distance between functionals of a compound Hawkes process given Gaussian density. To achieve this, rely Poisson embedding representation an for processes, more generally processes. As application, close gap in literature by providing first Berry-Ess\'een associated Central Limit Theorems process.