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

The functional quantization problem for one-dimensional Brownian diffusions on [0,T][0,T] is investigated. One shows under rather general assumptions that the rate of convergence of the LpLp-quantization error is O((logn)-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.