Dispersion of volume under the action of isotropic Brownian flows
Probability
2008-11-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0811.0276,
title = {Dispersion of volume under the action of isotropic Brownian flows},
author = {Georgi Dimitroff and Michael Scheutzow},
journal= {arXiv preprint arXiv:0811.0276},
year = {2008}
}
Comments
To appear in "Stochastic processes and their applications"