  The multilevel Monte Carlo (MLMC) method has been used for a wide variety of
stochastic applications. In this paper we consider its use in situations in
which input random variables can be replaced by similar approximate random
variables which can be computed much more cheaply. A nested MLMC approach is
adopted in which a two-level treatment of the approximated random variables is
embedded within a standard MLMC application. We analyse the resulting nested
MLMC variance in the specific context of an SDE discretisation in which Normal
random variables can be replaced by approximately Normal random variables, and
provide numerical results to support the analysis.
