Analysis of nested multilevel Monte Carlo using approximate Normal random variables

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 twolevel 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.