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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 (2020) Drift Estimation of Multiscale Diffusions Based on Filtered Data. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20201109-141017891

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Abstract

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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2009.13457arXivDiscussion Paper
ORCID:
AuthorORCID
Abdulle, Assyr0000-0002-5687-9742
Pavliotis, Grigorios A.0000-0002-3468-9227
Additional Information:AA, AZ and GG are partially supported by the Swiss National Science Foundation, under grant No. 200020_172710. The work of GAP 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. AMS is grateful to NSF (grant DMS 18189770) for financial support.
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200020_172710
Engineering and Physical Sciences Research Council (EPSRC)EP/P031587/1
JPMorgan Chase & Co.UNSPECIFIED
NSFDMS-18189770
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201109-141017891
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106564
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:09 Nov 2020 22:29
Last Modified:09 Nov 2020 22:29

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