## The Annals of Probability

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

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

#### 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