Non-central Limit Theorems for Non-linear Functionals of k Gaussian Fields

Let {X1n}, ..., {Xkn} be k stationary Gaussian processes. Suppose H is a functional of k variables. We are interested in the asymptotic distribution of the sequence [formula] where AN are appropriate forming constants and assuming that the correlation matrix tends slowly to 0. The limit distribution is given in terms of a non-Gaussian process for some H.