## The Annals of Applied Probability

### Motion in a Gaussian incompressible flow

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 7, Number 1 (1997), 229-264.

Dates
First available in Project Euclid: 14 October 2002

https://projecteuclid.org/euclid.aoap/1034625261

Digital Object Identifier
doi:10.1214/aoap/1034625261

Mathematical Reviews number (MathSciNet)
MR1428758

Zentralblatt MATH identifier
0880.60063

Subjects