  A general moment bound for sums of products of Gaussian vector's functions
extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general
central limit theorem for triangular arrays of nonlinear functionals of
multidimensional non-stationary Gaussian sequences is proved. This theorem
extends the previous results of Breuer and Major (1981), Arcones (1994) and
others. A Berry-Esseen-type bound in the above-mentioned central limit theorem
is derived following Nourdin, Peccati and Podolskij (2011). Two applications of
the above results are discussed. The first one refers to the asymptotic
behavior of a roughness statistic for continuous-time Gaussian processes and
the second one is a central limit theorem satisfied by long memory locally
stationary process.
