## The Annals of Probability

### The Poisson Approximation for Dependent Events

David Freedman

#### 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

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