  In this paper we study the properties of the Lasso estimator of the drift
component in the diffusion setting. More specifically, we consider a
multivariate parametric diffusion model $X$ observed continuously over the
interval $[0,T]$ and investigate drift estimation under sparsity constraints.
We allow the dimensions of the model and the parameter space to be large. We
obtain an oracle inequality for the Lasso estimator and derive an error bound
for the $L^2$-distance using concentration inequalities for linear functionals
of diffusion processes. The probabilistic part is based upon elements of
empirical processes theory and, in particular, on the chaining method.
