Remarks on Drift Estimation for Diffusion Processes
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 path-space density of the desired model equations, and through knowledge of the properties of quadratic variation. In this paper we show that the 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.
Additional Information
© 2009 Society for Industrial and Applied Mathematics. Received by the editors June 19, 2007; accepted for publication (in revised form) April 20, 2009; published electronically October 22, 2009.Attached Files
Published - 070694806.pdf
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Additional details
- Eprint ID
- 69484
- Resolver ID
- CaltechAUTHORS:20160805-152349945
- Created
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2016-08-08Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J79