STOCHASTIC MODEL REDUCTION FOR SLOW-FAST SYSTEMS WITH MODERATE TIME SCALE SEPARATION

We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with a moderate time scale separation. The stochastic model reduction strategy improves the approximation of systems with finite time scale separation, when compared to classical homogenization theory, by incorporating deviations from the infinite time scale limit considered in homogenization, as described by an Edgeworth expansion in the time scale separation parameter. To approximate these deviations from the limiting homogenized system in the reduced model, a surrogate system is constructed, the parameters of which are matched to produce the same Edgeworth expansion as in the original multiscale system. We corroborate the validity of our approach by numerical examples, showing significant improvements to classical homogenized model reduction.