The normal approximation rate for the drift estimator of multidimensional diffusions

We consider the problem of the density and drift estimation by the observation of a trajectory of an \mathbbR^d{\mathbb{R}^{d}}-dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type based on discretely sampled observations and study their asymptotic distribution. An estimate of the rate of normal approximation is given.