Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Luschgy, Harald; Pagès, Gilles License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-1446


Functional Quantization and Entropy for Stochastic Processes



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

  author =	{Luschgy, Harald and Pag\`{e}s, Gilles},
  title =	{{Functional Quantization and Entropy for Stochastic Processes}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-1446},
  doi =		{10.4230/DagSemProc.04401.4},
  annote =	{Keywords: Functional quantization , entropy , product quantizers}

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

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