Empirical and Gaussian processes on Besov classes

Details Empirical and Gaussian processes on Besov classes Empirical and Gaussian processes on Besov classes

2006-12-22

arxiv.org/abs/math/0612706v1

IMS Lecture Notes Monograph Series 2006, Vol. 51, 185-195

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000842 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000842

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.

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