Asymptotically optimal quantization schemes for Gaussian processes

Harald Luschgy (1) , Gilles Pagès (2) , Benedikt Wilbertz (1)

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

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.

Mots clés: Functional quantization; Gaussian process; Brownian Motion; Riemann-Liouville process; optimal quantizer

Domaines: Probabilités [math.PR]

Harald Luschgy, Gilles Pagès, Benedikt Wilbertz. Asymptotically optimal quantization schemes for Gaussian processes. ESAIM: Probability and Statistics, 2010, 14, 93-116 ; http://dx.doi.org/10.1051/ps:2008026. ⟨10.1051/ps:2008026⟩. ⟨hal-00258618⟩