Regularity and Crossings of Shot Noise Processes

Abstract : 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.
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Submitted on : Thursday, July 14, 2011 - 3:07:14 PM
Last modification on : Friday, September 20, 2019 - 4:34:02 PM
Long-term archiving on: Saturday, October 15, 2011 - 2:20:58 AM

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Hermine Biermé, Agnès Desolneux. Regularity and Crossings of Shot Noise Processes. 2011. ⟨hal-00484118v2⟩

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