The Annals of Applied Probability

On using the first difference in the Stein-Chen method

Aihua Xia

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Abstract

This paper investigates an alternative way of using the Stein-Chen method in Poisson approximations. There are three principal bounds stated in terms of reduced Palm probabilities for general point processes. The first two are for the accuracy of Poisson random variable approximation to the distribution of the number of points in a point process with respect to the total variation metric and the Wasserstein metric, and the third is for bounding the errors of Poisson process approximation to the distribution of a point process on a general compact space with respect to a Wasserstein metric. The bounds are frequently sharper than the previous results using the Stein-Chen method when the expected number of points is large.

Article information

Source
Ann. Appl. Probab., Volume 7, Number 4 (1997), 899-916.

Dates
First available in Project Euclid: 29 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1043862417

Digital Object Identifier
doi:10.1214/aoap/1043862417

Mathematical Reviews number (MathSciNet)
MR1484790

Zentralblatt MATH identifier
0903.60012

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60E17 60G55: Point processes

Keywords
Immigration-death process Stein-Chen method Palm distributions coupling

Citation

Xia, Aihua. On using the first difference in the Stein-Chen method. Ann. Appl. Probab. 7 (1997), no. 4, 899--916. doi:10.1214/aoap/1043862417. https://projecteuclid.org/euclid.aoap/1043862417


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