  In this paper, we provide upper bounds on the d2 distance between a large
class of functionals of a multivariate compound Hawkes process and a given
Gaussian vector. This is proven using Malliavin's calculus defined on an
underlying Poisson embedding. The upper bound is then used to infer the speed
of convergence of Central Limit Theorems for the multivariate compound Hawkes
process with exponential kernels as the observation time T goes to infinity.
