A general moment bound for a product of Gaussian vector's functionals and a central limit theorem for subordinated Gaussian triangular arrays

A general moment bound for a product of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A very general central limit theorem for triangular arrays of nonlinear functionals of multidimensional Gaussian sequences generalizing the results of Arcones (1994) is deduced. The stationarity of the Gaussian vector sequences is not required.