CROSSINGS OF SMOOTH SHOT NOISE PROCESSES
成果类型：
Article
署名作者：
Bierme, Hermine; Desolneux, Agnes
署名单位：
Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite de Tours
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/11-AAP807
发表日期：
2012
页码：
2240-2281
关键词：
摘要：
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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