The Annals of Probability

The Poisson Approximation for Dependent Events

David Freedman

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Abstract

Consider a sequence of dependent events, where each has uniformly small conditional probability given the past, and the sum of the conditional probabilities is approximately constant at $a$. Then the number of events which occur is approximately Poisson with parameter $a$. An explicit bound is given on the variation distance.

Article information

Source
Ann. Probab., Volume 2, Number 2 (1974), 256-269.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996707

Digital Object Identifier
doi:10.1214/aop/1176996707

Mathematical Reviews number (MathSciNet)
MR370694

Zentralblatt MATH identifier
0301.60021

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Poisson approximation stopping time invariance principle

Citation

Freedman, David. The Poisson Approximation for Dependent Events. Ann. Probab. 2 (1974), no. 2, 256--269. doi:10.1214/aop/1176996707. https://projecteuclid.org/euclid.aop/1176996707


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