Regularity and Crossings of Shot Noise Processes

Hermine Biermé (1) , Agnès Desolneux (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this paper, we consider shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the crossings mean number function is obtained through an integral formula. Moreover, as the intensity increases, or equivalently as the number of shots becomes larger, a normal convergence to the classical Rice's formula for Gaussian processes is obtained. The Gaussian kernel function is studied in detail and two different regimes are exhibited.

Mots clés: Shot noise; Crossings; Infinitely divisible process; Stationary process; Characteristic function; Poisson process

Domaines: Probabilités [math.PR]

Hermine Biermé, Agnès Desolneux. Regularity and Crossings of Shot Noise Processes. 2010. ⟨hal-00484118v1⟩