In this paper we present a novel approach towards variance reduction for
discretised diffusion processes. The proposed approach involves specially
constructed control variates and allows for a significant reduction in the
variance for the terminal functionals. In this way the complexity order of the
standard Monte Carlo algorithm (ε−3) can be reduced down to
ε−2∣log(ε)∣ in case of the Euler
scheme with ε being the precision to be achieved. These theoretical
results are illustrated by several numerical examples.Comment: arXiv admin note: text overlap with arXiv:1510.0314