## The Annals of Probability

- Ann. Probab.
- Volume 1, Number 3 (1973), 480-483.

### A Poisson-Type Limit Theorem for Mixing Sequences of Dependent 'Rare' Events

#### Abstract

Certain mixing sequences of dependent `rare' events are considered and a Poisson limit is established for the probability that $k$ events occur. An asymptotic distribution for the number of upcrossings of a high level by certain stochastic processes is considered as an application.

#### Article information

**Source**

Ann. Probab., Volume 1, Number 3 (1973), 480-483.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996941

**Digital Object Identifier**

doi:10.1214/aop/1176996941

**Mathematical Reviews number (MathSciNet)**

MR350816

**Zentralblatt MATH identifier**

0261.60023

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G10: Stationary processes

**Keywords**

Poisson process mixing `rare' events upcrossings weak convergence

#### Citation

Meyer, R. M. A Poisson-Type Limit Theorem for Mixing Sequences of Dependent 'Rare' Events. Ann. Probab. 1 (1973), no. 3, 480--483. doi:10.1214/aop/1176996941. https://projecteuclid.org/euclid.aop/1176996941