Communications in Mathematical Sciences
Volume 21 (2023)
Robust estimation of effective diffusions from multiscale data
Pages: 405 – 435
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.
parameter inference, diffusion processes, data-driven homogenization, filtering, Langevin equation
2010 Mathematics Subject Classification
60J60, 62F12, 62M05, 62M20, 65C30
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