Journal of Applied Mathematics
Volume 2010 (2010), Article ID 378519, 32 pages
Research Article

A Constructive Sharp Approach to Functional Quantization of Stochastic Processes

FB4-Department of Mathematics, University of Trier, 54286 Trier, Germany

Received 1 June 2010; Accepted 21 September 2010

Academic Editor: Peter Spreij

Copyright © 2010 Stefan Junglen and Harald Luschgy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.