Asymptotic behavior of the distortion-rate function for Gaussian processes in Banach spaces
type: Item
instance of: scholarly article
title: Asymptotic behavior of the distortion-rate function for Gaussian processes in Banach spaces
zbMATH Open document ID: 1090.60008
author: Steffen Dereich
published in: Bulletin des Sciences Mathématiques
publication date: 2006-03-08T00:00:00Z
review text: Let \(\mu\) be a Gaussian measure on a separable Banach space. The author proves that the logarithmic small ball probabilities of \(\mu\) are tightly related to some moment generating functions. Based upon this link a new lower bound for the distortion-rate function against the small ball function is derived. This allows to use results of the theory of small ball probabilities to deduce lower bounds for the distortion-rate function. As application one gets several sharp weak asymptotics for this rate function.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 5009824
zbMATH Keywords: High-resolution coding
zbMATH Keywords: small ball probabilities
MaRDI profile type: Publication
full work available at URL: j.bulsci.2005.04.001
OpenAlex ID: W1976793094
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DOI: 10.1016/J.BULSCI.2005.04.001
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description: scientific article; zbMATH DE number 5009824