The local quantization behavior of absolutely continuous probabilities

S. Graf , G. Pagès (1) , H. Luschgy

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L-r (P)-codebooks alpha(n), and any Voronoi partition V-n,V-a with respect to alpha(n) the local probabilities P(V-n,V-a) satisfy P(V-a,V-n) approximate to n(-1) while the local L-r-quantization errors satisfy integral V-n,V-a parallel to x - a parallel to(r) d P (x) approximate to n(-(1+r/d)) as long as the partition sets V-n,V-a intersect a fixed compact set K in the interior of the support of P.

Domaines: Probabilités [math.PR]

S. Graf, G. Pagès, H. Luschgy. The local quantization behavior of absolutely continuous probabilities. Annals of Probability, 2012, 40 (4), pp.1795-1828. ⟨10.1214/11-AOP663⟩. ⟨hal-00730490⟩