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Functional Quantization and Entropy for Stochastic Processes

Authors: Harald Luschgy and Gilles Pagès

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

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. PagÃƒÂ¨s, UniversitÃƒÂ© de Paris 6.

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Harald Luschgy and Gilles Pagès. Functional Quantization and Entropy for Stochastic Processes. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{luschgy_et_al:DagSemProc.04401.4,
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04401.4},
  URN =		{urn:nbn:de:0030-drops-1446},
  doi =		{10.4230/DagSemProc.04401.4},
  annote =	{Keywords: Functional quantization , entropy , product quantizers}
}

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DOI: 10.4230/DagSemProc.04401.15

Quantization of self-similar Probabilities

Authors: Siegfried Graf and Harald Luschgy

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

Abstract

The asymptotic behaviour of the quantization errors for self-similar probabilities is determined.

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Siegfried Graf and Harald Luschgy. Quantization of self-similar Probabilities. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{graf_et_al:DagSemProc.04401.15,
  author =	{Graf, Siegfried and Luschgy, Harald},
  title =	{{Quantization of self-similar Probabilities}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04401.15},
  URN =		{urn:nbn:de:0030-drops-1402},
  doi =		{10.4230/DagSemProc.04401.15},
  annote =	{Keywords: quantization , self-similar probabilities}
}

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Documents authored by Luschgy, Harald

Functional Quantization and Entropy for Stochastic Processes

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Quantization of self-similar Probabilities

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