Optimal quantizers for Radon random vectors in a Banach space

Siegried Graf (1) , Harald Luschgy (2) , Gilles Pagès (3)

1 UNIVERSITÄT PASSAU - Fakultät für Mathematik und Informatik
2 FB IV-Mathematik
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e_{n,r}(X,E) = inf{(E (\min_{a \in \alpha} || X-a ||^r )^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.

Mots clés: Functional quantization; optimal quantizer; stationary quantizer; stochastic process; intersection properties of balls

Domaines: Probabilités [math.PR]

Siegried Graf, Harald Luschgy, Gilles Pagès. Optimal quantizers for Radon random vectors in a Banach space. Journal of Approximation Theory, 2007, 144 (1), 27-53 ; http://dx.doi.org/10.1016/j.jat.2006.04.006. ⟨10.1016/j.jat.2006.04.006⟩. ⟨hal-00004668⟩