On the Mean Number of Crossings of a Level by a Stationary Gaussian Process

Abstract

Let $\xi (t)$ be a stationary Gaussian process and $N_\xi (u)$ denote the number of solutions of $\xi (t)=u, 0 \leqq t \leqq 1$. We prove the well-known formula for ${\bf M}_\xi (u)$ under conditions that are very close to the necessary ones.