Institute of Mathematical Statistics Lecture Notes - Monograph Series

Empirical and Gaussian processes on Besov classes

Richard Nickl

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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.

Chapter information

Source
Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn, eds., High Dimensional Probability: Proceedings of the Fourth International Conference (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 185-195

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284112

Digital Object Identifier
doi:10.1214/074921706000000842

Mathematical Reviews number (MathSciNet)
MR2387769

Zentralblatt MATH identifier
1156.60020

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Besov space Donsker class pregaussian class

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Nickl, Richard. Empirical and Gaussian processes on Besov classes. High Dimensional Probability, 185--195, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000842. https://projecteuclid.org/euclid.lnms/1196284112


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