Non-central limit theorems for non-linear functionals of vector valued Gaussian stationary random sequences

Our main problem is the description of possible limit theorems for non-linear functionals of vector valued Gaussian stationary random sequences. In the scalar valued case we have proved such a result with R.L. Dobrushin. Now we want to prove its multivariate version. We build up a correct theory about the Wiener-Ito integral representation of non-linear functionals of multivariate stationary Gaussian random sequences.