Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes.

Marie Kratz (1) , José Leon (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 Escuela de Matematicas [Caracas]

We propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process.

Mots clés: Hermite polynomial expansion; Gaussian processes; crossings; extremes; Hermite polynomial expansion.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Marie Kratz, José Leon. Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes.. Stochastic Processes and their Applications, 1997, 66 (2), pp.237-252. ⟨10.1016/S0304-4149(96)00122-6⟩. ⟨hal-00179412⟩