Functional Quantization and Entropy for Stochastic Processes

Luschgy, Harald; Pagès, Gilles

doi:10.4230/DagSemProc.04401.4

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Functional Quantization and Entropy for Stochastic Processes

Authors Harald Luschgy, Gilles Pagès

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 4401
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2005-04-19

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Document Identifiers

DOI: 10.4230/DagSemProc.04401.4
URN: urn:nbn:de:0030-drops-1446

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Keywords

Functional quantization
entropy
product quantizers

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/DagSemProc.04401.4

Author Details

Harald Luschgy

Gilles Pagès

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