Oracle inequalities for the stochastic differential equations

Abstract

This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi - martingale noises with jumps. The noises are modeled by the L\'evy processes, the Ornstein -- Uhlenbeck processes and semi-Markov processes. We represent the general model selection method and the sharp oracle inequalities methods which provide the robust efficient estimation in the adaptive setting. Moreover, we present the recent results on the improved model selection methods for the nonparametric estimation problems.