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Remarks on drift estimation for diffusion processes

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Pokern, Yvo, Stuart, A. M. and Vanden-Eijnden, Eric. (2009) Remarks on drift estimation for diffusion processes. Multiscale Modeling & Simulation, Vol.8 (No.1). pp. 69-95. ISSN 1540-3459

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Official URL: http://dx.doi.org/10.1137/070694806

Abstract

In applications such as molecular dynamics it is of interest to fit Smoluchowski and Langevin equations to data. Practitioners often achieve this by a variety of seemingly ad hoc procedures such as fitting to the empirical measure generated by the data, and fitting to properties of auto-correlation functions. Statisticians, on the other hand, often use estimation procedures which fit diffusion processes to data by applying the maximum likelihood principle to the path-space density of the desired model equations, and through knowledge of the properties of quadratic variation. In this note we show that these procedures used by practitioners and statisticians to fit drift functions are, in fact, closely related and can be thought of as two alternative ways to regularize the (singular) likelihood function for the drift. We also present the results of numerical experiments which probe the relative efficacy of the two approaches to model identification and compare them with other methods such as the minimum distance estimator.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Diffusion processes, Langevin equations, Parameter estimation, Molecular dynamics
Journal or Publication Title:	Multiscale Modeling & Simulation
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	1540-3459
Date:	2009
Volume:	Vol.8
Number:	No.1
Number of Pages:	27
Page Range:	pp. 69-95
Identification Number:	10.1137/070694806
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/3058