Asymptotically optimal quantization schemes for Gaussian processes

TitleAsymptotically optimal quantization schemes for Gaussian processes
Publication TypeJournal Article
Year of Publication2010
AuthorsHarald Luschgy, Gilles Pagès, and Benedikt Wilbertz
JournalESAIM: PS
Pagination93 - 116
KeywordsBrownian motion, functional quantization, Gaussian process, optimal quantizer, Riemann-Liouville process

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.