Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
Publié le : 2002-07-14
Classification:
Extreme values,
point processes,
compound Poisson process,
Stein's method,
60G55,
62E17,
60F05
@article{1029867135,
author = {Barbour, A. D. and M\aa nsson, Marianne},
title = {Compound Poisson process approximation},
journal = {Ann. Probab.},
volume = {30},
number = {1},
year = {2002},
pages = { 1492-1537},
language = {en},
url = {http://dml.mathdoc.fr/item/1029867135}
}
Barbour, A. D.; Månsson, Marianne. Compound Poisson process approximation. Ann. Probab., Tome 30 (2002) no. 1, pp. 1492-1537. http://gdmltest.u-ga.fr/item/1029867135/