Asymptotically optimal quantization schemes for gaussian processes on Hilbert spaces
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 93-116.

We describe quantization designs which lead to asymptotically and order optimal functional quantizers for gaussian processes in a Hilbert space setting. 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.

DOI : 10.1051/ps:2008026
Classification : 60G15, 60E99
Mots-clés : functional quantization, gaussian process, brownian motion, Riemann-Liouville process, optimal quantizer 
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     title = {Asymptotically optimal quantization schemes for gaussian processes on {Hilbert} spaces},
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Luschgy, Harald; Pagès, Gilles; Wilbertz, Benedikt. Asymptotically optimal quantization schemes for gaussian processes on Hilbert spaces. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 93-116. doi : 10.1051/ps:2008026. http://www.numdam.org/articles/10.1051/ps:2008026/

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