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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Entropy-constrained functional quantization of Gaussian processes


Authors: Siegfried Graf and Harald Luschgy
Journal: Proc. Amer. Math. Soc. 133 (2005), 3403-3409
MSC (2000): Primary 60G15, 94A24; Secondary 60B11, 94A34
Published electronically: May 2, 2005
MathSciNet review: 2161166
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Abstract: The sharp asymptotics for the entropy-constrained $L^2$-quantization errors of Gaussian measures on a Hilbert space and in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator.


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Additional Information

Siegfried Graf
Affiliation: Fakultät für Mathematik und Informatik, Universität Passau, D-94030 Passau, Germany
Email: graf@fmi.uni-passau.de

Harald Luschgy
Affiliation: FB IV-Mathematik, Universität Trier, D-54286 Trier, Germany
Email: luschgy@uni-trier.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07888-3
PII: S 0002-9939(05)07888-3
Keywords: Functional quantization, Gaussian process, entropy, distortion rate function
Received by editor(s): December 11, 2003
Received by editor(s) in revised form: June 14, 2004
Published electronically: May 2, 2005
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2005 American Mathematical Society