The Annals of Applied Probability

Crossings of smooth shot noise processes

Hermine Biermé and Agnès Desolneux

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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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Ann. Appl. Probab., Volume 22, Number 6 (2012), 2240-2281.

First available in Project Euclid: 23 November 2012

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Zentralblatt MATH identifier

Primary: 60G17: Sample path properties 60E07: Infinitely divisible distributions; stable distributions 60E10: Characteristic functions; other transforms
Secondary: 60G10: Stationary processes 60F05: Central limit and other weak theorems

Shot noise level crossings infinitely divisible process stationary process characteristic function Poisson process


Biermé, Hermine; Desolneux, Agnès. Crossings of smooth shot noise processes. Ann. Appl. Probab. 22 (2012), no. 6, 2240--2281. doi:10.1214/11-AAP807.

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