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Asymptotically optimal quantization schemes for Gaussian processes

Abstract : We describe quantization designs which lead to asymptotically and order optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions. Furthermore we derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes.
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Submitted on : Monday, February 25, 2008 - 6:29:37 PM
Last modification on : Monday, December 14, 2020 - 9:45:16 AM
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Harald Luschgy, Gilles Pagès, Benedikt Wilbertz. Asymptotically optimal quantization schemes for Gaussian processes. ESAIM: Probability and Statistics, EDP Sciences, 2010, 14, 93-116 ; http://dx.doi.org/10.1051/ps:2008026. ⟨10.1051/ps:2008026⟩. ⟨hal-00258618⟩

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