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Diffusion parameter estimation for the homogenized equation

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Manikas, Theodoros and Papavasiliou, Anastasia (2019) Diffusion parameter estimation for the homogenized equation. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 17 (2). pp. 675-695. doi:10.1137/18M120138X

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Official URL: https://doi.org/10.1137/18M120138X

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Abstract

We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research suggests subsampling the data on fixed intervals and computing the corresponding quadratic variation (see, for example, [19]). However, to achieve optimality, this approach requires knowledge of scale separation variable. Instead, we suggest computing the quadratic variation corresponding to the local extrema of the slow process. Our approach results to a natural subsampling and avoids the issue of choosing a subsampling rate. We prove that the estimator is asymptotically un-biased and we numerically demonstrate that its L2-error is smaller than the one achieved in.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Multiscale modeling, Applied mathematics, Parameter estimation, Mathematical statistics
Journal or Publication Title: Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal
Publisher: SIAM
ISSN: 1540-3459
Official Date: 30 April 2019
Dates:
DateEvent
30 April 2019Published
12 March 2019Accepted
Volume: 17
Number: 2
Page Range: pp. 675-695
DOI: 10.1137/18M120138X
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
RPG-2013-270Leverhulme Trusthttp://dx.doi.org/10.13039/501100000275
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