The Annals of Probability

A Central Limit Theorem for the Number of Zeros of a Stationary Gaussian Process

Jack Cuzick

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Abstract

Using a device which approximates stationary Gaussian processes by $M$-dependent processes, we find conditions on the covariance function to insure that the number of zero crossings, after centering and rescaling, has an asymptotically normal distribution. This device is then used to obtain central limit theorems for integrals of functions of stationary Gaussian processes.

Article information

Source
Ann. Probab., Volume 4, Number 4 (1976), 547-556.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996026

Digital Object Identifier
doi:10.1214/aop/1176996026

Mathematical Reviews number (MathSciNet)
MR420809

Zentralblatt MATH identifier
0348.60048

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G17: Sample path properties 60G10: Stationary processes 60G15: Gaussian processes

Keywords
Central limit theorem dependent random variables zero crossings Gaussian processes

Citation

Cuzick, Jack. A Central Limit Theorem for the Number of Zeros of a Stationary Gaussian Process. Ann. Probab. 4 (1976), no. 4, 547--556. doi:10.1214/aop/1176996026. https://projecteuclid.org/euclid.aop/1176996026


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