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تسجيل مستخدم جديدThe Malliavin-Stein method for Hawkes functionals
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In this paper, following Nourdin-Peccatis methodology, we combine the Malliavin calculus and Steins method to provide general bounds on the Wasserstein distance between functionals of a compound Hawkes process and a given Gaussian density. To achieve this, we rely on the Poisson embedding representation of an 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 the first Berry-Esseen bounds associated to Central Limit Theorems for the compound Hawkes process.
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