  In this paper we present new theoretical results for the Dantzig and Lasso
estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under
sparsity constraints. Our focus is on oracle inequalities for both estimators
and error bounds with respect to several norms. In the context of the Lasso
estimator our paper is strongly related to [11], who investigated the same
problem under row sparsity. We improve their rates and also prove the
restricted eigenvalue property solely under ergodicity assumption on the model.
Finally, we demonstrate a numerical analysis to uncover the finite sample
performance of the Dantzig and Lasso estimators.
