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Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*

Published online by Cambridge University Press:  10 May 2010

Harald Luschgy ,
Gilles Pagès  and
Benedikt Wilbertz
Harald Luschgy
Affiliation:
Universität Trier, FB IV-Mathematik, 54286 Trier, Germany
Gilles Pagès
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, Université Paris 6, Case Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05, France
Benedikt Wilbertz
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, Université Paris 6, Case Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05, France
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Abstract

We describe quantization designs which lead to asymptotically and order optimal functional quantizers for Gaussian processes in a Hilbert space setting. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions.

Keywords

Functional quantizationGaussian processBrownian motionRiemann-Liouville processoptimal quantizer
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 93 - 116
Copyright
© EDP Sciences, SMAI, 2010

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Footnotes

*

This work was supported in part by the AMaMeF Exchange Grant 1323 of the ESF.

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