The Annals of Applied Probability

On using the first difference in the Stein-Chen method

Aihua Xia

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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

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

First available in Project Euclid: 29 January 2003

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Zentralblatt MATH identifier

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

Immigration-death process Stein-Chen method Palm distributions coupling


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.

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