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February 1997 Motion in a Gaussian incompressible flow
Tomasz Komorowski, George Papanicolaou
Ann. Appl. Probab. 7(1): 229-264 (February 1997). DOI: 10.1214/aoap/1034625261

Abstract

We prove that the solution of a system of random ordinary differential equations $d\mathbf{X}(t)/dt = \mathbf{V}(t, \mathbf{X}(t))$ with diffusive scaling, $\mathbf{X}_{\varepsilon}(t) = \varepsilon \mathbf{X}(t/ \varepsilon^2)$, converges weakly to a Brownian motion when $\varepsilon \downarrow 0$. We assume that $\mathbf{V}(t, \mathbf{x}), t \epsilon R, \mathbf{x} \epsilon R^d$ is a d-dimensional, random, incompressible, stationary Gaussian field which has mean zero and decorrelates in finite time.

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Tomasz Komorowski. George Papanicolaou. "Motion in a Gaussian incompressible flow." Ann. Appl. Probab. 7 (1) 229 - 264, February 1997. https://doi.org/10.1214/aoap/1034625261

Information

Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0880.60063
MathSciNet: MR1428758
Digital Object Identifier: 10.1214/aoap/1034625261

Subjects:
Primary: 60H25
Secondary: 62M40

Keywords: diffusion approximation , mixing condition , Random field , weak convergence

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 1 • February 1997
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