Slepian model based independent interval approximation for the level excursion distributions

2024/10/08 by Bengtsson, Henrik, Podgorski, Krzysztof
#60G10 (Primary) 60G15 #60G70 (Secondary) #60K15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.06000

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.

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