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November 1997 On using the first difference in the Stein-Chen method
Aihua Xia
Ann. Appl. Probab. 7(4): 899-916 (November 1997). DOI: 10.1214/aoap/1043862417


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.


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Aihua Xia. "On using the first difference in the Stein-Chen method." Ann. Appl. Probab. 7 (4) 899 - 916, November 1997.


Published: November 1997
First available in Project Euclid: 29 January 2003

zbMATH: 0903.60012
MathSciNet: MR1484790
Digital Object Identifier: 10.1214/aoap/1043862417

Primary: 60E15
Secondary: 60E17 , 60G55

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

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 4 • November 1997
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