This paper investigates an alternative way of using the Stein-Chen
method in Poisson approximations. There are three principal bounds stated in
terms of reduced Palm probabilities for general point processes. The first two
are for the accuracy of Poisson random variable approximation to the
distribution of the number of points in a point process with respect to the
total variation metric and the Wasserstein metric, and the third is for
bounding the errors of Poisson process approximation to the distribution of a
point process on a general compact space with respect to a Wasserstein metric.
The bounds are frequently sharper than the previous results using the
Stein-Chen method when the expected number of points is large.
@article{1043862417,
author = {Xia, Aihua},
title = {On using the first difference in the Stein-Chen method},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 899-916},
language = {en},
url = {http://dml.mathdoc.fr/item/1043862417}
}
Xia, Aihua. On using the first difference in the Stein-Chen method. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 899-916. http://gdmltest.u-ga.fr/item/1043862417/