Empirical and Gaussian processes on Besov classes

Abstract

We give several conditions for pregaussianity of norm balls of Besov spaces defined over $\mathbb{R}^d$ by exploiting results in Haroske and Triebel (2005). Furthermore, complementing sufficient conditions in Nickl and P\"{o}tscher (2005), we give necessary conditions on the parameters of the Besov space to obtain the Donsker property of such balls. For certain parameter combinations Besov balls are shown to be pregaussian but not Donsker.