Title: Exceedance time distributions through the clipped Slepian process
Authors: Henrik Bengtsson - Lund University (Sweden) [presenting]
Abstract: In physics and engineering literature, the distribution of the excursion time distribution for a stationary Gaussian process has been approximated by a stationary switch process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switch process. We propose a similar but alternative matching of the expected value of the clipped Slepian process and the corresponding switch process initiated at zero. The method has several advantages over its original, stationary matching version. First, for a large class of processes, it produces a valid distribution for the excursion time, while the stationary version never leads to a valid distribution. Another advantage is when used for the non-zero excursion levels since it can utilize both the up-crossing Slepian model and the down-crossing one leading to natural approximations of the distributions of excursions above and below the given level.