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

• DOI: 10.48550/arxiv.1907.09162
• Publication Date: 2019-01-01
• Authors: Martin Magris
• Keywords: FOS: Computer and information sciences; Probability (math.PR); Econometrics (econ.EM); 02 engineering and technology; Statistics - Computation; Methodology (stat.ME); FOS: Economics and business; 0202 electrical engineering, electronic engineering, information engineering; FOS: Mathematics; Mathematics - Probability; Statistics - Methodology; Computation (stat.CO); Economics - Econometrics

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