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.