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Drift Estimation of Multiscale Diffusions Based on Filtered Data

Abdulle, Assyr and Garegnani, Giacomo and Pavliotis, Grigorios A. and Stuart, Andrew M. and Zanoni, Andrea (2021) Drift Estimation of Multiscale Diffusions Based on Filtered Data. Foundations of Computational Mathematics . ISSN 1615-3375. doi:10.1007/s10208-021-09541-9. (In Press)

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We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coefficient of the homogenized equation requires pre-processing of the data, often in the form of subsampling; this is because the two-scale equation and the homogenized single-scale equation are incompatible at small scales, generating mutually singular measures on the path space. We avoid subsampling and work instead with filtered data, found by application of an appropriate kernel function, and compute maximum likelihood estimators based on the filtered process. We show that the estimators we propose are asymptotically unbiased and demonstrate numerically the advantages of our method with respect to subsampling. Finally, we show how our filtered data methodology can be combined with Bayesian techniques and provide a full uncertainty quantification of the inference procedure.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Abdulle, Assyr0000-0002-5687-9742
Garegnani, Giacomo0000-0001-7700-1157
Pavliotis, Grigorios A.0000-0002-3468-9227
Stuart, Andrew M.0000-0001-9091-7266
Additional Information:© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit Received 28 September 2020; Revised 27 April 2021; Accepted 04 June 2021; Published 13 October 2021. We thank the anonymous reviewers whose comments helped improve and clarify this manuscript. Assyr Abdulle, Andrea Zanoni and Giacomo Garegnani are partially supported by the Swiss National Science Foundation, under Grant No. 200020_172710. The work of Grigorios A. Pavliotis was partially funded by the EPSRC, Grant Number EP/P031587/1, and by JPMorgan Chase & Co. Any views or opinions expressed herein are solely those of the authors listed, and may differ from the views and opinions expressed by JPMorgan Chase & Co. or its affiliates. This material is not a product of the Research Department of J.P. Morgan Securities LLC. This material does not constitute a solicitation or offer in any jurisdiction. Andrew M. Stuart is grateful to NSF (Grant DMS 18189770) for financial support. Open Access funding provided by EPFL Lausanne. Dedicated to the memory of Assyr Abdulle. Communicated by Wolfgang Dahmen.
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200020_172710
Engineering and Physical Sciences Research Council (EPSRC)EP/P031587/1
Subject Keywords:Parameter inference; Diffusion process; Data-driven homogenization; Filtering; Bayesian inference; Langevin equation
Classification Code:AMS subject classifications. 62F15, 65C30, 62M05, 74Q10
Record Number:CaltechAUTHORS:20201109-141017891
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Official Citation:Abdulle, A., Garegnani, G., Pavliotis, G.A. et al. Drift Estimation of Multiscale Diffusions Based on Filtered Data. Found Comput Math (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106564
Deposited By: George Porter
Deposited On:09 Nov 2020 22:29
Last Modified:29 Oct 2021 18:28

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