  The aim of this paper is to provide a comprehensive introduction for the
study of L1-penalized estimators in the context of dependent observations. We
define a general $\ell_{1}$-penalized estimator for solving problems of
stochastic optimization. This estimator turns out to be the LASSO in the
regression estimation setting. Powerful theoretical guarantees on the
statistical performances of the LASSO were provided in recent papers, however,
they usually only deal with the iid case. Here, we study our estimator under
various dependence assumptions.
