A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations

We present and analyze a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time scale of indi- vidual 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 vari- ables forward in time. The new microscopic state, consistent with the extrapolated variables, is obtained by a matching operator that minimizes the perturbation caused by the extrapolation. We provide a proof of the convergence of this method, in the absence of statistical error, and we analyze various strategies for matching, as an operator on probability measures. Numerical experiments we show illustrate the effects of the different approximations on the resulting error in macroscopic predictions.