We study the functional estimation of the space-dependent diffusion coefficient in a one-dimensional framework. The sample path is observed at discrete times. We study global [math] -loss errors [math] over Besov spaces [math] . We show that, under suitable conditions, the minimax rate of convergence is the usual [math] . Linking our model to nonparametric regression, we provide an estimating procedure based on a linear wavelet method which is optimal in the minimax sense.
Publié le : 1999-06-14
Classification:
Besov spaces,
diffusion processes,
local time,
minimax estimation,
nonparametric regression,
wavelets on the internal,
wavelet orthonormal bases
@article{1172617199,
author = {Hofmann, Marc},
title = {Lp estimation of the diffusion coefficient},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 447-481},
language = {en},
url = {http://dml.mathdoc.fr/item/1172617199}
}
Hofmann, Marc. Lp estimation of the diffusion coefficient. Bernoulli, Tome 5 (1999) no. 6, pp. 447-481. http://gdmltest.u-ga.fr/item/1172617199/