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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

Funded by The Danish National Research Foundation

MPS-RR 2004-16
July 2004

Perfect Simulation of Hawkes Processes

by: Jakob G. Rasmussen , Jesper Møller


This article concerns a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structure, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. Examples of applications and empirical results are presented.

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