Study of micro–macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise

摘要: Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of slowest dynamics. This paper looks efficiency micro-macro acceleration method that couples short bursts path simulation with extrapolation spatial averages forward in time. To have explicit derivations, we elicit an amenable linear test equation containing multiple scales. We make derivations and perform numerical experiments Gaussian setting, where only evolution mean variance matters. The analysis shows that, for this model, stability threshold step is largely independent separation. In consequence, increases admissible steps far beyond those which direct discretization becomes unstable.