  We present and analyze a micro/macro acceleration technique for the Monte
Carlo simulation of stochastic differential equations (SDEs) in which there is
a separation between the (fast) time-scale on which individual trajectories of
the SDE need to be simulated and the (slow) time-scale on which we want to
observe the (macroscopic) function of interest. The method performs short
bursts of microscopic simulation using an ensemble of SDE realizations, after
which the ensemble is restricted to a number of macroscopic state variables.
The resulting macroscopic state is then extrapolated forward in time and the
ensemble is projected onto the extrapolated macroscopic state. We provide a
first analysis of its convergence in terms of extrapolation time step and
number of macroscopic state variables. The effects of the different
approximations on the resulting error are illustrated via numerical
experiments.
