This article is cited in 4 papers

Short Communications

Conditions for moments of the number of zeroes of Gaussian stationary processes to be finite

R. N. Mirošin

A. A. Ždanov Leningrad State University

Abstract: We deal with factorial moments $N_m(t)$ of the number of zeroes of a Gaussian stationary process $\xi_{\tau}$, $\mathbf M\xi_{\tau}=0$, $\tau\in[0,t]$. For $\xi_t$ having the property of local non-determinism of order $k$ (Definition 1), necessary and sufficient conditions for moments $N_m(t)$ to be finite are obtained (Theorems 1 and 2). In Theorems 3 and 4 these conditions are simplified for the case $k=1$.

Received: 15.07.1974
Revised: 30.09.1975

 English version: Theory of Probability and its Applications, 1978, 22:3, 615–625

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