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The Stein-Chen method, point processes and compensators


Barbour, A D; Brown, T (1992). The Stein-Chen method, point processes and compensators. The Annals of Probability, 20(3):1504-1527.

Abstract

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.

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Stein-Chen method; point process; compensator; Palm probability; martingale; Poisson approximation
Language:English
Date:1992
Deposited On:04 Mar 2010 10:24
Last Modified:20 Feb 2018 13:03
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/aop/1176989704

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