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

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 efficient alternatives. This manuscript shows that the ITS approach can be conveniently discussed in terms of Lambert-W functions. An optimized and efficient implementation suggests that this approach is computationally more performing than more recent alternatives available for the simulation of the Hawkes process.