Representations into the Itô-Wiener Chaos and asymptotic results such as CLTs are obtained for the curve-crossings number of a stationary Gaussian process according to the form of the curve. Applications in physics and sea modelling follow, with the study of the estimator of the natural frequency of a harmonic oscillator and the study of specular points.
KRATZ, M. et LEON, J.R. (2010). Level Curves Crossings and Applications for Gaussian Models. Extremes, 13(3), pp. 315-351.