Crossings of smooth Shot Noise Processes

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.
Document type :
Journal articles
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2012, 22 (6), pp.2240--2281
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00589560
Contributor : Hermine Biermé <>
Submitted on : Friday, April 29, 2011 - 11:50:39 AM
Last modification on : Friday, February 10, 2017 - 8:38:48 AM
Document(s) archivé(s) le : Saturday, July 30, 2011 - 2:42:52 AM

File

SmoothShotpreprint.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00589560, version 1

Collections

Citation

Hermine Biermé, Agnès Desolneux. Crossings of smooth Shot Noise Processes. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2012, 22 (6), pp.2240--2281. <hal-00589560>

Share

Metrics

Record views

187

Document downloads

83