| Title | Asymptotically optimal quantization schemes for Gaussian processes | 
| Publication Type | Journal Article | 
| Year of Publication | 2010 | 
| Authors | Harald Luschgy, Gilles Pagès, and Benedikt Wilbertz | 
| Journal | ESAIM: PS | 
| Volume | 14 | 
| Pagination | 93 - 116 | 
| Keywords | Brownian motion, functional quantization, Gaussian process, optimal quantizer, Riemann-Liouville process | 
| 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   |  
          
-quantization errors of Riemann-Liouville processes.