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Perfect Simulation of Hawkes Processes
Jesper Møller and Jakob G. Rasmussen
Advances in Applied Probability
Vol. 37, No. 3 (Sep., 2005), pp. 629-646
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/30037347
Page Count: 18
You can always find the topics here!Topics: Simulations, Cumulative distribution functions, Edge effects, Poisson process, Algorithms, Earthquakes, Distributivity, Statistical models, Statism, Approximation
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Our objective is to construct 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 structures, 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. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.
Advances in Applied Probability © 2005 Applied Probability Trust