Poisson perturbations

Free access article

Issue		ESAIM: PS Volume 3, 1999


Page(s)		131 - 150
DOI		10.1051/ps:1999106

DOI: 10.1051/ps:1999106

ESAIM: PS, October 1999, Vol. 3, p. 131-150

Poisson perturbations

Perturbations de Poisson

Andrew D. Barbour
Abteilung für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland; (adb@amath.unizh.ch)

Aihua Xia
Department of Statistics, School of Mathematics, The University of New South Wales, Sydney 2052, Australia.

Received January 28, 1999. Revised July 26, 1999.

Abstract: Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Cekanavicius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.

Résumé: On utilise la méthode de Stein pour approximer, par rapport à la variation totale, la distribution d'une variable aléatoire aux valeurs entières par une mesure (éventuellement signée) de Poisson composée. Pour les sommes de variables aléatoires indépendantes, on obtient des résultats très explicites ; les estimations de la précision de l'approximation, construites à l'aide de la méthode de "coupling'', sont plus exactes que celles de Kruopis (1983) et de Cekanivicius (1997). Un exemple sert à illustrer le potentiel de la méthode envers les sommes de variables aléatoires dépendantes.

Keywords and phrases: Stein's method, signed compound Poisson measure, total variation, coupling.

AMS Subject Classification: 62E17, 60G50, 60F05.

Article without figures.

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