Approximate Simulation of Hawkes Processes

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Lecture Notes: Temporal Point Processes and the Conditional Intensity Function (2018, methodology): “So the Hawkes process can be simulated either by the inverse method or Ogata’s modified thinning algorithm (but in fact there are simpler methods for simulating the Hawkes process, see e.g. Møller and Rasmussen (2005, 2006)).”
Exact simulation of Hawkes process with exponentially decaying intensity (2013, methodology): “For statistical analysis or practical implementations, simulation is a crucial issue as the procedure of the parameter estimation or calibration, in particular, for higher ∗Department of Statistics, London School of Economics, United Kingdom.”
Perfect simulation of Hawkes processes (2005, methodology): “However, as indicated by the plots and verified in [18], limt→0 Gn(t) < 1 when G = 0, meaning that Gn is not a CDF.”