Slepian models for chi²-processes with dependent components with application to envelope upcrossings

A Slepian model for the local behaviour near the level upcrossings of a chi²-process with dependent Gaussian components is presented. In case of independent components, this model is shown to take on a rather simple form, thereby simplifying earlier results by Aronowich and Adler. The Slepian model is applied to the envelope of a stationary Gaussian process and used to approximate the probability of "empty" envelope upcrossings, i.e. the probability that an envelope upcrossing is not followed by a level crossing in the original process