Non asymptotic sharp oracle inequalities for high dimensional ergodic diffusion models. *

In this paper we consider high dimensional ergodic diffusion models in nonparametric setting on the basis of discrete data, when the diffusion coefficients are unknown. For this problem, by using efficient sequential point-wise estimators we construct a model selection procedure and then we show sharp oracle inequalities, i.e. the inequalities in which the main term coefficient is closed to one. This means that the proposed sequential model selection procedure is optimal in this sense. Particularly, we show that the constructed procedure is the best in the class of weighted least square estimators with the Pinsker coefficients which provide the efficient estimation in the minimal asymptotical quadratic risk sense