The paper gives bounds for the accuracy of Poisson approximation to the distribution of the number of points in a point process. There are two principal bounds, one in terms of reduced Palm probabilities for general point processes, and one involving compensators for point processes on the line. The latter bound is frequently sharper than the previously used compensator bounds when the expected number of points is large, and examples show that little improvement is possible without changing the form of the bound.
Publié le : 1992-07-14
Classification:
Stein-Chen method,
point process,
compensator,
Palm probability,
martingale,
Poisson approximation,
60G55,
60E15,
60G44,
60J75
@article{1176989704,
author = {Barbour, A. D. and Brown, Timothy C.},
title = {The Stein-Chen Method, Point Processes and Compensators},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1504-1527},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989704}
}
Barbour, A. D.; Brown, Timothy C. The Stein-Chen Method, Point Processes and Compensators. Ann. Probab., Tome 20 (1992) no. 4, pp. 1504-1527. http://gdmltest.u-ga.fr/item/1176989704/