Sharp asymptotics of the functional quantization problem for Gaussian processes.
type: Item
instance of: scholarly article
title: Sharp asymptotics of the functional quantization problem for Gaussian processes.
zbMATH Open document ID: 1049.60029
DOI: 10.1214/009117904000000324
author: Harald Luschgy
author: Gilles Pagès
published in: The Annals of Probability
publication date: 2004-09-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0410156
review text: The authors obtain the sharp asymptotic for the \(L^2\)-quantization error of Gaussian measures on a Hilbert space. Numerous examples of applications for Gaussian processes and fields are given. Recent results on quantization are discussed.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 94A24
Mathematics Subject Classification ID: 94A34
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 2100704
zbMATH Keywords: high-resolution
zbMATH Keywords: quantization
zbMATH Keywords: Shannon entropy
zbMATH Keywords: Gaussian process
reviewed by: Andriy Olenko
MaRDI profile type: Publication
OpenAlex ID: W3106535967
arXiv ID: math/0410156
cites work: Q5598243
cites work: Q4726487
cites work: On the&lt;tex&gt;epsilon&lt;/tex&gt;-entropy of certain Gaussian processes
cites work: Small ball constants and tight eigenvalue asymptotics for fractional Brownian motions
cites work: Q4391441
cites work: Small ball probabilities around random centers of Gaussian measures and applications to quantization
cites work: On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces
cites work: On the Bernstein-von Mises theorem with infinite-dimensional parameters
cites work: Integrated Brownian motions and exact \(L_2\)-small balls
cites work: Q4271995
cites work: Foundations of quantization for probability distributions
cites work: Functional quantization and small ball probabilities for Gaussian processes
cites work: Quantization
cites work: On ε-Entropy of Equivalent Gaussian Processes
cites work: Q4003734
cites work: Functional quantization of Gaussian processes
cites work: On the average complexity of multivariate problems
cites work: Average-case analysis of numerical problems
cites work: Q5586702
cites work: Q3679095
cites work: Q5801644
cites work: Interpolation of spatial data. Some theory for kriging
description: scientific article