Maximum likelihood drift estimation for multiscale diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Papavasiliou, A.²  Pavliotis, G. A.¹  Stuart, A. M.³ 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[3] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

关键词: Multiscale diffusions;    Averaging;    Homogenization;    Maximum likelihood;   

DOI  :  10.1016/j.spa.2009.05.003

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free