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

摘要

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. (C) 2005 Elsevier B.V. All rights reserved.