# Functional quantization and metric entropy for Riemann-Liouville processes

Abstract : We derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.
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Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00004281
Contributor : Gilles Pagès <>
Submitted on : Thursday, February 17, 2005 - 2:55:58 PM
Last modification on : Wednesday, December 9, 2020 - 3:12:10 PM
Long-term archiving on: : Thursday, April 1, 2010 - 8:35:50 PM

### Citation

Harald Luschgy, Gilles Pagès. Functional quantization and metric entropy for Riemann-Liouville processes. 2005. ⟨hal-00004281⟩

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