Papavasiliou, Anastasia, Pavliotis, G. A. and Stuart, A. M.. (2009) Maximum likelihood drift estimation for multiscale diffusions. Stochastic Processes and their Applications, Vol.119 (No.10). pp. 3173-3210. ISSN 0304-4149

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Abstract

We Study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we refer to as averaging and homogenization problems. We ask whether, given data from the slow variable in the fast/slow system, we can correctly estimate parameters in the drift of the coarse-grained equation For the slow variable, using maximum likelihood. We show that, whereas the maximum likelihood estimator is asymptotically unbiased for the averaging problem, for the homogenization problem maximum likelihood fails unless we subsample the data at an appropriate rate. An explicit formula For the asymptotic error in the log-likelihood function is presented. Our theory is applied to two simple examples from molecular dynamics. (C) 2009 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics Faculty of Science > Statistics
Journal or Publication Title:	Stochastic Processes and their Applications
Publisher:	Elsevier Science BV
ISSN:	0304-4149
Date:	October 2009
Volume:	Vol.119
Number:	No.10
Number of Pages:	38
Page Range:	pp. 3173-3210
Identification Number:	10.1016/j.spa.2009.05.003
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/17141

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