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On the rate of Poisson process approximation to a Bernoulli process

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  14 July 2016

P. S. Ruzankin
P. S. Ruzankin*
Affiliation:
Sobolev Institute of Mathematics of the Russian Academy of Sciences
*
∗ Postal address: Sobolev Institute of Mathematics, Acad. Koptyug prospect 4, Novosibirsk 630090, Russia. Email address: [email protected]
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Abstract

The main result of the paper is a refinement of Xia's (1997) bound on the Kantorovich distance between distributions of a Bernoulli point process and an approximating Poisson process. In particular, we show that the distance between distributions of a Bernoulli point process and the Poisson process with the same mean measure has the order of the total variation distance between the laws of the total masses of these processes.

Keywords

Poisson approximation of point processesBernoulli processcoupling

MSC classification

Primary: 60G55: Point processes
Secondary: 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 271 - 276
Copyright
Copyright © Applied Probability Trust 2004 

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