The Annals of Probability

The Stein-Chen Method, Point Processes and Compensators

A. D. Barbour and Timothy C. Brown

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 20, Number 3 (1992), 1504-1527.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989704

Digital Object Identifier
doi:10.1214/aop/1176989704

Mathematical Reviews number (MathSciNet)
MR1175275

Zentralblatt MATH identifier
0770.60052

JSTOR
links.jstor.org

Subjects
Primary: 60G55: Point processes
Secondary: 60E15: Inequalities; stochastic orderings 60G44: Martingales with continuous parameter 60J75: Jump processes

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

Citation

Barbour, A. D.; Brown, Timothy C. The Stein-Chen Method, Point Processes and Compensators. Ann. Probab. 20 (1992), no. 3, 1504--1527. doi:10.1214/aop/1176989704. https://projecteuclid.org/euclid.aop/1176989704


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