Homogenization has been widely used in stochastic model reduction of slow-fast systems, including geophysical and climate systems. The theory relies on an infinite time scale separation. In this talk we present results for the realistic case of finite time scale separation. In particular, we employ Edgeworth expansions as finite size corrections to the central limit theorem and show improved performance of the reduced stochastic models in numerical simulations.
This is joint work with Jeroen Wouters.