Drift estimation for Brownian flows

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:73

Article

Piterbarg, L

关键词: diffusion;    maximum likelihood;    estimation;    Lagrangian data;    stochastic flow;   

DOI  :  10.1016/S0304-4149(97)00097-5

来源: Elsevier

【 摘 要 】

The problem of estimating the drift of a stochastic flow given Lagrangian observations is an estimation problem for a multidimensional diffusion with a degenerate diffusion matrix. The maximum-likelihood estimator of the constant drift is considered. A long-time asymptotic of its mean-square error (MSE) is computed. It is shown that the time-space average of the observed Lagrangian velocities has the same asymptotic. These estimators are compared to the least-squares estimator based on Eulerian data. In the most important, for applications, two-dimensional case the Lagrangian estimator is typically preferable for incompressible flows, while for flows close to potential the Eulerian estimator is better. (C) 1998 Elsevier Science B.V. All rights reserved.

【 授权许可】

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