On some reliability applications of Rice's formula for the intensity of level crossings
The author proves that the Rice formula for the expected number of crossing a fixed level \(u\) by a stationary Gaussian process \(X(t)\) holds for almost all \(u\) if \(E |\dot X(0)|<\infty\). The proof is based on the Banach theorem which relates the variation of a function and the number of crossings of a fixed level by the graph of this function. It is demonstrated that this a.s. result is sufficient for applications in modeling the size of stress due to slams that occur when a ship proceeds in rough seas, a wave crest height and a fatigue of metals.
scientific article; zbMATH DE number 1833852