We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646–659] that, under mild assumptions, the transformed processes behave approximately like Poisson processes for large T. In this article, under very similar assumptions, explicit upper bounds are given for the d2-distance between the corresponding point process distributions. A number of related results, and applications to kernel density estimation and long range dependence testing are also presented. The main results are proved by applying a generalized Stein–Chen method to discretized versions of the point processes.
Publié le : 2005-02-14
Classification:
Point processes,
Poisson process approximation,
Stein’s method,
density estimation,
total variation distance,
dt₂-distance,
60G55,
62E20,
62G07
@article{1107271662,
author = {Schuhmacher, Dominic},
title = {Upper bounds for spatial point process approximations},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 615-651},
language = {en},
url = {http://dml.mathdoc.fr/item/1107271662}
}
Schuhmacher, Dominic. Upper bounds for spatial point process approximations. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 615-651. http://gdmltest.u-ga.fr/item/1107271662/