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Luschgy, Harald ; PagŤs, Gilles

Functional Quantization and Entropy for Stochastic Processes

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


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 =	{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 =		{},
  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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