  Our goal is to establish large deviations and concentration inequalities for
the maximum likelihood estimator of the drift parameter of the
Ornstein-Uhlenbeck process without tears. We propose a new strategy to
establish large deviation results which allows us, via a suitable
transformation, to circumvent the classical difficulty of non-steepness. Our
approach holds in the stable case where the process is positive recurrent as
well as in the unstable and explosive cases where the process is respectively
null recurrent and transient. Notwithstanding of this trichotomy, we also
provide new concentration inequalities for the maximum likelihood estimator.
