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Maximum likelihood estimator for the drift of a Brownian flow
Author(s) -
Çag̃lar Mi̇ne
Publication year - 2000
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/(sici)1526-4025(200001/03)16:1<23::aid-asmb377>3.0.co;2-3
Subject(s) - estimator , mathematics , statistics , maximum likelihood , econometrics , statistical physics , physics
The maximum likelihood estimator for the drift of a Brownian flow on ℝ d , d ⩾ 2, is found with the assumption that the covariance is known. By approximation of the drift with known functions, the statistical model is reduced to a parametric one that is a curved exponential family. The data is the n ‐point motion of the Brownian flow throughout the time interval [0, T ]. The asymptotic properties of the MLE are also investigated. Copyright © 2000 John Wiley & Sons, Ltd.