Slepian model based independent interval approximation for the level excursion distributions

TL;DR

This paper introduces a Slepian model-based method for approximating the distributions of level excursions in Gaussian processes, extending the classical independent interval approximation to non-zero levels with a solid probabilistic foundation.

Contribution

It develops a novel Slepian model approach for level excursion distributions, especially for non-zero crossings, enhancing the theoretical understanding and accuracy of approximations.

Findings

The method matches the expected value of the clipped Slepian to a non-stationary process.

It extends the approximation to non-zero crossings, providing a probabilistic basis.

The approach is shown to differ from classical IIA for non-zero levels.

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.