Open Access
July, 1992 The Stein-Chen Method, Point Processes and Compensators
A. D. Barbour, Timothy C. Brown
Ann. Probab. 20(3): 1504-1527 (July, 1992). DOI: 10.1214/aop/1176989704


The paper gives bounds for the accuracy of Poisson approximation to the distribution of the number of points in a point process. There are two principal bounds, one in terms of reduced Palm probabilities for general point processes, and one involving compensators for point processes on the line. The latter bound is frequently sharper than the previously used compensator bounds when the expected number of points is large, and examples show that little improvement is possible without changing the form of the bound.


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A. D. Barbour. Timothy C. Brown. "The Stein-Chen Method, Point Processes and Compensators." Ann. Probab. 20 (3) 1504 - 1527, July, 1992.


Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0770.60052
MathSciNet: MR1175275
Digital Object Identifier: 10.1214/aop/1176989704

Primary: 60G55
Secondary: 60E15 , 60G44 , 60J75

Keywords: compensator , martingale , Palm probability , point process , Poisson approximation , Stein-Chen method

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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