Kolmogorov Distance for Multivariate Normal Approximation

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar<TEX>e</TEX>(B) Probab.Statist. 46(1) (2010) 45-98].