An Ergodic Theorem on the Distribution of the Duration of Fades

The duration of fades of a stationary process is the time interval between the crossing of a fixed level from below going upwards to the next crossing of this level from above going downwards.
It follows from [1], that the conditional distribution $F(x)$ of the duration of fades exists if the crossing from below going upwards was at the origin of the time axis. It is proved in the paper that for an ergodic process the relative number of fades of duration less than X on the time interval $[0,T]$ tends to $F(x)$ as $T\to\infty$.