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

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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
Keywords: functional quantization, gaussian process, brownian motion, Riemann-Liouville process, optimal quantizer 
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     author = {Luschgy, Harald and Pag\`es, Gilles and Wilbertz, Benedikt},
     title = {Asymptotically optimal quantization schemes for gaussian processes on {Hilbert} spaces},
     journal = {ESAIM: Probability and Statistics},
     pages = {93--116},
     publisher = {EDP-Sciences},
     volume = {14},
     year = {2010},
     doi = {10.1051/ps:2008026},
     mrnumber = {2654549},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008026/}
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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

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