| Issue |
ESAIM: PS
Volume 14, 2010
|
|
|---|---|---|
| Page(s) | 93 - 116 | |
| DOI | https://doi.org/10.1051/ps:2008026 | |
| Published online | 10 May 2010 | |
Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*
1
Universität Trier, FB IV-Mathematik, 54286 Trier, Germany
2
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, Université Paris 6, Case Courrier 188, 4
place Jussieu, 75252 Paris Cedex 05, France
Corresponding authors: luschgy@uni-trier.de gpa@ccr.jussieu.fr wilbertz@uni-trier.de
Received:
22
November
2007
Revised:
5
May
2008
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.
Mathematics Subject Classification: 60G15 / 60E99
Key words: Functional quantization / Gaussian process / Brownian motion / Riemann-Liouville process / optimal quantizer
© EDP Sciences, SMAI, 2010
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