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Register a new userMalliavin-Stein method for the multivariate compound Hawkes process
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Authors
Mahmoud Khabou
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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 Malliavins 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.
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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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