Nonparametric estimation for I.I.D. paths of fractional SDE

This paper deals with nonparametric estimators of the drift function b computed from independent continuous observations, on a compact time interval, solution stochastic differential equation driven by fractional Brownian motion (fSDE). First, risk bound is established Skorokhod’s integral based least squares oracle $${\widehat{b}}$$ b. Thanks to relationship between fSDE and its derivative respect initial condition, deduced calculable approximation . Another directly an estimator $$b'$$ for comparison. The consistency rates convergence are these in case compactly supported trigonometric basis or $${\mathbb {R}}$$ -supported Hermite basis.