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Several methods have been developed for the simulation of the Hawkes process.The oldest approach is the inverse sampling transform (ITS) suggested in\citep{ozaki1979maximum}, but rapidly abandoned in favor of more efficientalternatives. This manuscript shows that the ITS approach can be convenientlydiscussed in terms of Lambert-W functions. An optimized and efficientimplementation suggests that this approach is computationally more performingthan more recent alternatives available for the simulation of the Hawkesprocess.

On the simulation of the Hawkes process via Lambert-W functions