On the acceleration of the multi-level Monte Carlo method

The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor (p/α)² if weak approximation methods of orders α and p are applied in the case of computational costs growing with the same order as the variances decay.