Robust estimation of effective diffusions from multiscale data

We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is asymptotically unbiased with respect to the theory of homogenization. Moreover, we demonstrate on a range of challenging numerical experiments that our method is accurate in extracting coarse-grained dynamics from multiscale data. In particular, the estimators we propose are more robust and require less knowledge of the full model than the standard technique of subsampling, which is widely employed in practice in this setting.

Keywords

parameter inference, diffusion processes, data-driven homogenization, filtering, Langevin equation

2010 Mathematics Subject Classification

60J60, 62F12, 62M05, 62M20, 65C30

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The authors are partially supported by the Swiss National Science Foundation, under grant No. 200020 172710.

Received 8 September 2021

Received revised 21 January 2022

Accepted 29 May 2022

Published 1 February 2023