Asymptotically optimal quantization schemes for Gaussian processes

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Luschgy, Harald
Pagès, Gilles
Wilbertz, Benedikt
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Abstract
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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.
Comment: 25
Keywords
Mathematics - Probability, 60G15, 60E99
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