Approximation, Metric Entropy and Small Ball Estimates for Gaussian Measures (1999)
| Venue: | Ann. Probab |
| Citations: | 30 - 14 self |
BibTeX
@ARTICLE{Li99approximation,metric,
author = {Wenbo V. Li and Werner Linde},
title = {Approximation, Metric Entropy and Small Ball Estimates for Gaussian Measures},
journal = {Ann. Probab},
year = {1999},
volume = {27},
pages = {1556--1578}
}
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Abstract
A precise link proved by J. Kuelbs and W. V. Li relates the small ball behavior of a Gaussian measure on a Banach space E with the metric entropy behavior of K , the unit ball of the RKHS of in E. We remove the main regularity assumption imposed on the unknown function in the link. This enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates for concrete Gaussian processes. Moreover, we show that the small ball behavior of a Gaussian process is also tightly connected with the speed of approximation by "nite rank" processes. Abbreviated title: Metric Entropy and Small Ball Estimates Keywords: Gaussian process, small deviation, metric entropy, approximation number. AMS 1991 Subject Classications: Primary: 60G15 ; Secondary: 60F99, 47D50, 47G10 . 1 Supported in part by NSF 1 1 Introduction Let denote a centered Gaussian measure on a real separable B...
