Level curves, crossings and specular points for Gaussian models.

Marie Kratz (1, 2, 3) , José R. Leon (4)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 ESSEC Business School
4 Escuela de Matematicas [Caracas]

Using generalizations of the well known Rice formula and applying the general method related to m-dependent processes that we settled in earlier works, allow one to obtain representations into the Ito-Wiener Chaos and CLTs for curve-crossings number. This approach not only explains heuristic considerations of Longuet-Higgins on specular points and related problems in the context of sea modelling, but goes far beyond when providing asymptotic results. These results on curve-crossings may also be applied in other fields. One example is the study of the estimator of the natural frequency of a harmonic oscillator.

Mots clés: co-area formula; crossings; CLT; Gaussian fields; Hermite polynomials; level curve; (generalized) Rice formula; specular point.; specular point

Domaines: Probabilités [math.PR]

Marie Kratz, José R. Leon. Level curves, crossings and specular points for Gaussian models.. 2007. ⟨hal-00239290v2⟩