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

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.