A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
For researchers simulating stochastic systems with multiple time scales, this method reduces computational cost while maintaining accuracy, though it is an incremental improvement over existing multiscale methods.
The paper introduces a micro-macro acceleration method for Monte Carlo simulation of SDEs with time-scale separation, combining short path simulations with extrapolation of macroscopic state variables. It provides a convergence proof and numerical experiments showing error effects.
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.