  We aim at analyzing in terms of a.s. convergence and weak rate the
performances of the Multilevel Monte Carlo estimator (MLMC) introduced in
[Gil08] and of its weighted version, the Multilevel Richardson Romberg
estimator (ML2R), introduced in [LP14]. These two estimators permit to compute
a very accurate approximation of $I_0 = \mathbb{E}[Y_0]$ by a Monte Carlo type
estimator when the (non-degenerate) random variable $Y_0 \in L^2(\mathbb{P})$
cannot be simulated (exactly) at a reasonable computational cost whereas a
family of simulatable approximations $(Y_h)_{h \in \mathcal{H}}$ is available.
We will carry out these investigations in an abstract framework before applying
our results, mainly a Strong Law of Large Numbers and a Central Limit Theorem,
to some typical fields of applications: discretization schemes of diffusions
and nested Monte Carlo.
