The Annals of Probability

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

R. M. Meyer

Full-text: Open access

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


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