We use the Poisson cluster process structure of a Hawkes process to
derive non asymptotic estimates of the tail of the
extinction time, of the coupling time or of the number of points per
interval. This allows us to define a family of independent Hawkes
processes; each of them approximating the initial process on a
particular interval. Then we can
easily derive exponential inequalities for Hawkes processes which
can precise the ergodic theorem.
Publié le : 2007-01-14
Classification:
Point processes,
exponential inequalities,
approximate simulation of a stationary Hawkes process,
60G55
@article{1170347811,
author = {Reynaud-Bouret, Patricia and Roy, Emmanuel},
title = {Some non asymptotic tail estimates for Hawkes processes},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 883-896},
language = {en},
url = {http://dml.mathdoc.fr/item/1170347811}
}
Reynaud-Bouret, Patricia; Roy, Emmanuel. Some non asymptotic tail estimates for Hawkes processes. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 883-896. http://gdmltest.u-ga.fr/item/1170347811/