Abstract
We study the functional estimation of the space dependent diffusion coefficient, for a global L p-loss over Besov spaces, when the sample path is discretely observed on the time interval [0, 1]. We show that under a suitable assumption on the local time of the diffusion process, the minimax rate of convergence is n − sp/(1+2s) as in classical situations, such as density estimation or nonparametric regression. We propose a wavelet estimator achieving the optimal rate of convergence.
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