Slepian model based independent interval approximation for the level excursion distributions

Abstract

The independent interval approximation of the excursion time distributions for Gaussian processes has been used in physics and engineering. A new but related approach matches the expected value of the clipped Slepian to the expected value of a non-stationary binary stochastic process. This approach is extended to non-zero crossings and provides a probabilistic foundation for the validity of the approximations for a large class of processes. Both the above and below distributions are approximated. While the Slepian-based method was shown to be equivalent to the classical IIA for the zero-level, this is not the case for non-zero excursions.