Dispersion of volume under the action of isotropic Brownian flows

Details Dispersion of volume under the action of isotropic Brownian flows Dispersion of volume under the action of isotropic Brownian flows

2008-11-03

arxiv.org/abs/0811.0276v1

Mathematics

Probability

To appear in "Stochastic processes and their applications"

Scientific paper

We study transport properties of isotropic Brownian flows. Under a transience condition for the two-point motion, we show asymptotic normality of the image of a finite measure under the flow and -- under slightly stronger assumptions -- asymptotic normality of the distribution of the volume of the image of a set under the flow. Finally, we show that for a class of isotropic flows, the volume of the image of a nonempty open set (which is a martingale) converges to a random variable which is almost surely strictly positive.

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