Recursive computation of the Hawkes cumulants

We propose a recursive method for the computation of cumulants self-exciting point processes Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement higher-order in comparison with existing methods differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply joint generated multidimensional processes.