Home » Publications

Functional quantization of a class of Brownian diffusions: a constructive approach

TitleFunctional quantization of a class of Brownian diffusions: a constructive approach
Publication TypeJournal Article
Year of Publication2006
AuthorsHarald Luschgy, and Gilles Pagès
JournalStochastic Processes and their Applications
Volume116
Pagination310 - 336
ISSN0304-4149
KeywordsBrownian diffusions, functional quantization, Lamperti transform; Girsanov theorem, optimal quantizers
Abstract

The functional quantization problem for one-dimensional Brownian diffusions on $ [0,T] $ is investigated. One shows under rather general assumptions that the rate of convergence of the $ L^p $-quantization error is $ O(\log(n)^{-1/2}) $ like for the Brownian motion. Several methods to construct some rate-optimal quantizers are proposed. These results are extended to $ d $-dimensional diffusions when the diffusion coefficient is the inverse of a gradient function. Finally, a special attention is given to diffusions with a Gaussian martingale term.