## The Annals of Probability

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

### The Poisson Approximation for Dependent Events

#### 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