Robust Estimation of Effective Diffusions from Multiscale Data

We present a methodology based on filtered data and moving averages for estimating robustly effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that the method we propose is asymptotically unbiased with respect to homogenization theory. Moreover, we demonstrate with a series of numerical experiments that the method we propose here outperforms traditional techniques for extracting coarse-grained dynamics from data, such as subsampling, in terms of bias and of robustness.