Journal
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
Volume 8, Issue 1, Pages 53-64Publisher
SPRINGER
DOI: 10.1007/s11009-006-7288-z
Keywords
edge effects; Hawkes process; marked point process; Poisson cluster process; simulation
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Hawkes processes are important in point process theory and its applications, and simulation of such processes are often needed for various statistical purposes. This article concerns a simulation algorithm for unmarked and marked Hawkes processes, exploiting that the process can be constructed as a Poisson cluster process. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work Moller and Rasmussen (2004). We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical results for the algorithm compared with perfect simulations. Extensions of the algorithm and the results to more general types of marked point processes are also discussed.
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