| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: The functional quantization problem for one-dimensional Brownian diffusions on $[0,T]$ is investigated. First, the existence of optimal $n$-quantizers for every $n\ge 1$ is established, based on an existence result for random vectors taking their values in abstract Banach spaces. Then, one shows under rather general assumptions that the rate of convergence of the $L^p$-quantization error is $O((\log n) ^{-\frac 12})$ like for the Brownian motion. Several methods to construct some quasi-optimal quantizers are proposed. Finally, a special attention is given to diffusions with a Gaussian martingale term.
Mots Clés: Functional quantization ; optimal quantizers ; Brownian diffusions ;
Lamperti transform ; Girsanov Theorem
Date: 2003-10-15
Prépublication numéro: PMA-853