Title: 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 Lévy 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.