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In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between the law of functionals of a compound Hawkes process and the one of a Gaussian random variable. To achieve this, we rely on the Poisson imbedding representation of a Hawkes process to provide a Malliavin calculus for the Hawkes processes, and more generally for compound Hawkes processes. As an application, we close a gap in the literature by providing a quantitative Central Limit Theorem for the compound Hawkes process. [ABSTRACT FROM AUTHOR]

We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Among several examples, we provide an application to a functional version of the Breuer-Major CLT for fields subordinated to a fractional Brownian motion. [ABSTRACT FROM AUTHOR]