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Remarks on drift estimation for diffusion processes
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Pokern, Yvo, Stuart, A. M. and VandenEijnden, Eric. (2009) Remarks on drift estimation for diffusion processes. Multiscale Modeling & Simulation, Vol.8 (No.1). pp. 6995. ISSN 15403459
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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
autocorrelation functions. Statisticians, on the other hand, often use estimation procedures which fit
diffusion processes to data by applying the maximum likelihood principle to the pathspace 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:  15403459  
Official Date:  2009  
Dates: 


Volume:  Vol.8  
Number:  No.1  
Number of Pages:  27  
Page Range:  pp. 6995  
Identification Number:  10.1137/070694806  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
References:  [1] F. M. Bandi and P. C. B. Phillips, Fully nonparametric estimation of scalar diffusion models, 

URI:  http://wrap.warwick.ac.uk/id/eprint/3058 
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