@article {25, title = {Functional quantization of a class of Brownian diffusions: a constructive approach}, journal = {Stochastic Processes and their Applications}, volume = {116}, number = {2}, year = {2006}, pages = {310 - 336}, 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.}, keywords = {Brownian diffusions, functional quantization, Lamperti transform; Girsanov theorem, optimal quantizers}, issn = {0304-4149}, author = {Harald Luschgy and Gilles Pag{\`e}s} }