  We present and analyse a micro-macro acceleration method for the Monte Carlo
simulation of stochastic differential equations with separation between the
(fast) time-scale of individual trajectories and the (slow) time-scale of the
macroscopic function of interest. The algorithm combines short bursts of path
simulations with extrapolation of a number of macroscopic state variables
forward in time. The new microscopic state, consistent with the extrapolated
variables, is obtained by a matching operator that minimises the perturbation
caused by the extrapolation. We provide a proof of the convergence of this
method, in the absence of statistical error, and we analyse various strategies
for matching, as an operator on probability measures. Finally, we present
numerical experiments that illustrate the effects of the different
approximations on the resulting error in macroscopic predictions.
