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URN: urn:nbn:de:0030-drops-1446
URL: https://drops.dagstuhl.de/opus/volltexte/2005/144/
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Luschgy, Harald ; Pagès, Gilles

Functional Quantization and Entropy for Stochastic Processes

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04401.LuschgyHarald.Paper.144.pdf (0.3 MB)


Abstract

Let X be a Gaussian process and let U denote the
Strassen ball of X. A precise link between the
L^2-quantization error of X and the Kolmogorov
(metric) entropy of U in a Hilbert space setting
is established. In particular, the sharp
asymptotics of the Kolmogorov entropy problem is
derived. The condition imposed is regular
variation of the eigenvalues of the covariance
operator. Good computable quantizers for Gaussian
and diffusion processes and their numerical
efficieny are discussed.
This is joint work with G. Pagès, Université de Paris 6.

BibTeX - Entry

@InProceedings{luschgy_et_al:DSP:2005:144,
  author =	{Harald Luschgy and Gilles Pag{\`e}s},
  title =	{Functional Quantization and Entropy for Stochastic Processes},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  year =	{2005},
  editor =	{Thomas M{\"u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  number =	{04401},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/144},
  annote =	{Keywords: Functional quantization , entropy , product quantizers}
}

Keywords: Functional quantization , entropy , product quantizers
Collection: 04401 - Algorithms and Complexity for Continuous Problems
Issue Date: 2005
Date of publication: 19.04.2005


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