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.
Keywords: functional quantization, gaussian process, brownian motion, Riemann-Liouville process, optimal quantizer
@article{PS_2010__14__93_0,
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},
year = {2010},
publisher = {EDP Sciences},
volume = {14},
doi = {10.1051/ps:2008026},
mrnumber = {2654549},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps:2008026/}
}
TY - JOUR AU - Luschgy, Harald AU - Pagès, Gilles AU - Wilbertz, Benedikt TI - Asymptotically optimal quantization schemes for gaussian processes on Hilbert spaces JO - ESAIM: Probability and Statistics PY - 2010 SP - 93 EP - 116 VL - 14 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps:2008026/ DO - 10.1051/ps:2008026 LA - en ID - PS_2010__14__93_0 ER -
%0 Journal Article %A Luschgy, Harald %A Pagès, Gilles %A Wilbertz, Benedikt %T Asymptotically optimal quantization schemes for gaussian processes on Hilbert spaces %J ESAIM: Probability and Statistics %D 2010 %P 93-116 %V 14 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps:2008026/ %R 10.1051/ps:2008026 %G en %F PS_2010__14__93_0
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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