  We consider a dynamical system with small noise for which the drift is
parametrized by a finite dimensional parameter. For this model we consider
minimum distance estimation from continuous time observations under
$l^p$-penalty imposed on the parameters in the spirit of the Lasso approach
with the aim of simultaneous estimation and model selection. We study the
consistency and the asymptotic distribution of these Lasso-type estimators for
different values of $p$. For $p=1$ we also consider the adaptive version of the
Lasso estimator and establish its oracle properties.
