Volume 14, 2010
|Page(s)||93 - 116|
|Published online||10 May 2010|
Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*
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
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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