This repository contains Maple, Mathematica and SageMath codes for the computation of the (multidimensional joint) moments and cumulants of all orders of Hawkes processes with exponential kernels, as described in the references below.
Some of the codes also apply to the computation of moments and cumulants of stochastic integrals of deterministic functions with respect to (multidimentional) Hawkes processes.
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N. Privault and M. Thieullen, Closed-form modeling of neuronal spike train statistics by multivariate Hawkes processes, Physical Review E 106 (2022).
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N. Privault, An algorithm for the computation of joint Hawkes moments with exponential kernel, Proceedings of the 53rd ISCIE International Symposium on Stochastic Systems Theory and Its Applications (SSS’21).
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N. Privault, Recursive computation of the Hawkes cumulants, Statistics & Probability Letters 177 (2021).