Kuelbs–Li Inequalities and Metric Entropy of Convex Hulls

Oliver Kley ()
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Oliver Kley: Friedrich-Schiller-Universität Jena

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 649-665

Abstract: Abstract Let T be a precompact subset of a Hilbert space. We make use of a precise link between the absolutely convex hull $\operatorname{aco}(T)$ and the reproducing kernel Hilbert space of a Gaussian random variable constructed from T. Firstly, we avail ourselves of it for optimality considerations concerning the well-known Kuelbs–Li inequalities. Secondly, this enables us to apply small deviation results to the problem of estimating the metric entropy of $\operatorname{aco}(T)$ in dependence of the metric entropy of T.

Keywords: Metric entropy; Convex hull; Gaussian process; Small deviations; Reproducing kernel Hilbert space; 60G15; 47B06; 52A99; 46C05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-012-0408-5

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