The Annals of Applied Probability

Crossings of smooth shot noise processes

Hermine Biermé and Agnès Desolneux

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1353695953

Digital Object Identifier
doi:10.1214/11-AAP807

Mathematical Reviews number (MathSciNet)
MR3024968

Zentralblatt MATH identifier
1278.60073

Subjects
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

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

Citation

Biermé, Hermine; Desolneux, Agnès. Crossings of smooth shot noise processes. Ann. Appl. Probab. 22 (2012), no. 6, 2240--2281. doi:10.1214/11-AAP807. https://projecteuclid.org/euclid.aoap/1353695953


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