%0 Journal Article %1 moller_approximate_2006 %A Møller, Jesper %A Rasmussen, Jakob G. %D 2006 %J Methodology and Computing in Applied Probability %K Edge Hawkes Marked Poisson Simulation cluster effects, point process, processes %N 1 %P 53--64 %R 10.1007/s11009-006-7288-z %T Approximate Simulation of Hawkes Processes %U https://doi.org/10.1007/s11009-006-7288-z %V 8 %X 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 Møller 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.

@article{moller_approximate_2006, abstract = {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 M{\o}ller 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.}, added-at = {2020-01-31T19:19:18.000+0100}, author = {M{\o}ller, Jesper and Rasmussen, Jakob G.}, biburl = {https://www.bibsonomy.org/bibtex/20729151050815223b3aa553f653210e3/mannbachm}, doi = {10.1007/s11009-006-7288-z}, file = {Springer Full Text PDF:C\:\\Users\\Jan\\Zotero\\storage\\XCUAX28B\\M{\o}ller and Rasmussen - 2006 - Approximate Simulation of Hawkes Processes.pdf:application/pdf}, interhash = {be332158c8f401aa585dbdd4f88cc5de}, intrahash = {0729151050815223b3aa553f653210e3}, issn = {1573-7713}, journal = {Methodology and Computing in Applied Probability}, keywords = {Edge Hawkes Marked Poisson Simulation cluster effects, point process, processes}, language = {en}, month = mar, number = 1, pages = {53--64}, timestamp = {2020-01-31T19:20:14.000+0100}, title = {Approximate {Simulation} of {Hawkes} {Processes}}, url = {https://doi.org/10.1007/s11009-006-7288-z}, urldate = {2019-10-28}, volume = 8, year = 2006 }