Upcrossing probabilities for stationary Gaussian processes

Abstract

JAMES PICKANDS IIIO 1. Introduction. Let {X(t), -co<t<co} be a separable, measurable version of a continuous stationary Gaussian stochastic process. In what follows, it will be assumed, without loss of generality, that (1.1) EX(t) = 0, EX2(t) = 1.