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

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 $k=1$.