Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Abdulle:2023:10.1007/s10208-021-09541-9,
author = {Abdulle, A and Garegnani, G and Pavliotis, GA and Stuart, AM and Zanoni, A},
doi = {10.1007/s10208-021-09541-9},
journal = {Foundations of Computational Mathematics},
pages = {33--84},
title = {Drift estimation of multiscale diffusions based on filtered data},
url = {http://dx.doi.org/10.1007/s10208-021-09541-9},
volume = {23},
year = {2023}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Abdulle,A
AU  - Garegnani,G
AU  - Pavliotis,GA
AU  - Stuart,AM
AU  - Zanoni,A
DO  - 10.1007/s10208-021-09541-9
EP  - 84
PY  - 2023///
SN  - 1615-3375
SP  - 33
TI  - Drift estimation of multiscale diffusions based on filtered data
T2  - Foundations of Computational Mathematics
UR  - http://dx.doi.org/10.1007/s10208-021-09541-9
UR  - https://link.springer.com/article/10.1007%2Fs10208-021-09541-9
UR  - http://hdl.handle.net/10044/1/92277
VL  - 23
ER  -
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