Functional quantization and metric entropy for Riemann-Liouville processes

Harald Luschgy (1) , Gilles Pagès (2)

1 FB IV-Mathematik
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.

Mots clés: Functional quantization; metric entropy; Gaussian process; Riemann-Liouville process; optimal quantizer

Domaines: Probabilités [math.PR]

Harald Luschgy, Gilles Pagès. Functional quantization and metric entropy for Riemann-Liouville processes. 2005. ⟨hal-00004281⟩