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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

Aihua Xia
Aihua Xia*
Affiliation:
University of New South Wales
*
∗ Postal address: Department of Statistics, School of Mathematics, The University of New South Wales, Sydney 2052, Australia.
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Abstract

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

Keywords

IMMIGRATION–DEATH PROCESSSTEIN'S METHODPALM DISTRIBUTIONSCOUPLING

MSC classification

Primary: 60G55: Point processes 60E15: Inequalities; stochastic orderings

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 898 - 907
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This work was supported by a 1995 Australia Research Council Small Grant from the University of New South Wales.

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