Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156692 | Stochastic Processes and their Applications | 2006 | 27 Pages |
Abstract
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Harald Luschgy, Gilles Pagès,