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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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WRAP-Diffusion-parameter-estimation-homogenized-equation-Papavasiliou-2019.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (674Kb) |
Official URL: https://doi.org/10.1137/18M120138X
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 | ||||||
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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: |
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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 | ||||||
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