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December 2012 Crossings of smooth shot noise processes
Hermine Biermé, Agnès Desolneux
Ann. Appl. Probab. 22(6): 2240-2281 (December 2012). DOI: 10.1214/11-AAP807


In this paper, we consider smooth shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the mean number of crossings 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, that corresponds to many applications in physics, is studied in detail and two different regimes are exhibited.


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Hermine Biermé. Agnès Desolneux. "Crossings of smooth shot noise processes." Ann. Appl. Probab. 22 (6) 2240 - 2281, December 2012.


Published: December 2012
First available in Project Euclid: 23 November 2012

zbMATH: 1278.60073
MathSciNet: MR3024968
Digital Object Identifier: 10.1214/11-AAP807

Primary: 60E07 , 60E10 , 60G17
Secondary: 60F05 , 60G10

Keywords: Characteristic function , infinitely divisible process , level crossings , Poisson process , Shot noise , stationary process

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.22 • No. 6 • December 2012
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