Dispersion of volume under the action of isotropic Brownian flows

G. Dimitroff and M. Scheutzow

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 588-601

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: Stochastic; differential; equation; Stochastic; flow; Isotropic; Brownian; flow; Vague; convergence; Asymptotic; normality (search for similar items in EconPapers)
Date: 2009
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