@article {45, title = {Asymptotically optimal quantization schemes for Gaussian processes}, journal = {ESAIM: PS}, volume = {14}, year = {2010}, pages = {93 - 116}, abstract = {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.}, keywords = {Brownian motion, functional quantization, Gaussian process, optimal quantizer, Riemann-Liouville process}, author = {Harald Luschgy and Gilles Pag{\`e}s and Benedikt Wilbertz} }