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VOL. 51 | 2006 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 Pötscher (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.

Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1156.60020
MathSciNet: MR2387769

Digital Object Identifier: 10.1214/074921706000000842

Subjects:
Primary: 60F17
Secondary: 46E35

Rights: Copyright © 2006, Institute of Mathematical Statistics

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