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In this paper, we consider smooth shot noise processes and their expectednumber of level crossings. When the kernel response function is sufficientlysmooth, the mean number of crossings function is obtained through an integralformula. Moreover, as the intensity increases, or equivalently, as the numberof shots becomes larger, a normal convergence to the classical Rice's formulafor Gaussian processes is obtained. The Gaussian kernel function, thatcorresponds to many applications in physics, is studied in detail and twodifferent regimes are exhibited.

Crossings of smooth shot noise processes