Multilevel Monte Carlo methods, developed independently by Stefan Heinrich and Mike Giles in different stochastic contexts, can be viewed as a hierarchical control variate approach to reducing the computational cost of Monte Carlo simulation.
In many applications, an expected value can be estimated with root-mean-square accuracy ε at a computational cost which is O(ε-2).

This presentation will begin by emphasising the simplicity of the approach, and the way in which the theory gives the optimal number of samples to be computed on each level of approximation.  After a quick overview of the range of applications being pursued by various research groups, and some very interesting new extensions to the theory, I will then discuss two new applications which I am working on, one concerning the modelling of the stochastic motion of polymers in a liquid, and the other concerned with computing expected exit times and associated output functionals for Brownian diffusions.