Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields

We introduce a general method, which combines the one developed by authors in 1997 and one derived from the work of Malevich, Cuzick and mainly Berman, to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field.

KRATZ, M. and LEON, J. (2001). Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields. Journal of Theoretical Probability, 14(3), pp. 639-672.

Keywords : #AMS-classification, #asymptotic-variance, #central-limit-theorem, #crossings, #Gaussian-fields, #Gaussian-processes, #Hermite-polynomials, #level-curve, #maxima, #sojourn-time