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.

翻译：在本文中,我们考虑了平滑的噪音过程及其预期的跨越水平数量。当内核反应功能足够平稳时,通过一个整体公式获得平均的过境功能数量。 此外,随着强度增加,或随着射击次数的增加而相应增加,我们获得了与古典赖斯的高斯过程公式的正常趋同。 与物理的许多应用相对应的高斯内核功能得到了详细研究,并展示了两种不同的制度。