We propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process.
KRATZ, M. et LEON, J. (1997). Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes. Stochastic Processes and their Applications, 66(2), pp. 237-252.