On the Normal Stationary Process--Areas Outside Given Levels

Abstract

Let $x(t)$ be a normal stationary process, observed for $0 \leqslant t \leqslant T$, and $c$ a given positive constant. Formulae are derived for the mean and variance of the area above the level $+ c$ formed by the process $x(t)$ in $(0,T)$. Corresponding results are obtained for the sum and the difference of the areas above the level $+ c$ and below the level $- c$