High extremes of Gaussian chaos processes. A discrete time approximation approach

We consider a Gaussian zero-mean stationary vector process and a homogeneous function of a positive order of the given vector process. We study probabilities of high extrema of the resulting Gaussian chaos process. We present the principal methods of our investigations which are the Laplace asymptotic method and the Double Sum method when we first pass to the discrete time with refining time grid and then use appropriate approximation results.