A sufficient condition for the number of zeros of a differentiable Gaussian stationary process to be finite

We are concerned with factorial moments $N_m(T)$ of the number of zeros of a Gaussian stationary process $\xi_t$, $\mathbf M\xi_t=0$, $t\in[0,T]$. For $\xi_t$ having the derivative $\xi'_t$, a sufficient condition for moments $N_m(T)$ to be finite is obtained (Theorem 1). In theorems 2 and 3 we deal with applications of Theorem 1 to concrete classes of $\xi_t$.