Abstract
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 L p -loss errors ( 1≤p<+∞) over Besov spaces B sp ∞ . We show that, under suitable conditions, the minimax rate of convergence is the usual n - s/(1+2s) . Linking our model to nonparametric regression, we provide an estimating procedure based on a linear wavelet method which is optimal in the minimax sense.
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