Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*

Harald Luschgy; Gilles Pagès; Benedikt Wilbertz

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 93-116
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Luschgy, Harald, Pagès, Gilles, and Wilbertz, Benedikt. "Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*." ESAIM: Probability and Statistics 14 (2010): 93-116. <http://eudml.org/doc/250845>.

@article{Luschgy2010,
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. },
author = {Luschgy, Harald, Pagès, Gilles, Wilbertz, Benedikt},
journal = {ESAIM: Probability and Statistics},
keywords = {Functional quantization; Gaussian process; Brownian motion; Riemann-Liouville process; optimal quantizer; functional quantization; Gaussian measures in Hilbert spaces; Riemann-Liouville process},
language = {eng},
month = {5},
pages = {93-116},
publisher = {EDP Sciences},
title = {Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*},
url = {http://eudml.org/doc/250845},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Luschgy, Harald
AU - Pagès, Gilles
AU - Wilbertz, Benedikt
TI - Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*
JO - ESAIM: Probability and Statistics
DA - 2010/5//
PB - EDP Sciences
VL - 14
SP - 93
EP - 116
AB - 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.
LA - eng
KW - Functional quantization; Gaussian process; Brownian motion; Riemann-Liouville process; optimal quantizer; functional quantization; Gaussian measures in Hilbert spaces; Riemann-Liouville process
UR - http://eudml.org/doc/250845
ER -

References

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