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August, 1976 A Central Limit Theorem for the Number of Zeros of a Stationary Gaussian Process
Jack Cuzick
Ann. Probab. 4(4): 547-556 (August, 1976). DOI: 10.1214/aop/1176996026

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.

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Jack Cuzick. "A Central Limit Theorem for the Number of Zeros of a Stationary Gaussian Process." Ann. Probab. 4 (4) 547 - 556, August, 1976. https://doi.org/10.1214/aop/1176996026

Information

Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0348.60048
MathSciNet: MR420809
Digital Object Identifier: 10.1214/aop/1176996026

Subjects:
Primary: 60F05
Secondary: 60G10, 60G15, 60G17

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 4 • August, 1976
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