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Drift estimation for Brownian flows

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  • Piterbarg, L.

Abstract

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.

Suggested Citation

  • Piterbarg, L., 1998. "Drift estimation for Brownian flows," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 131-149, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:131-149
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