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Dispersion of volume under the action of isotropic Brownian flows

Author

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  • Dimitroff, G.
  • Scheutzow, M.

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.

Suggested Citation

  • Dimitroff, G. & Scheutzow, M., 2009. "Dispersion of volume under the action of isotropic Brownian flows," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 588-601, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:588-601
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    References listed on IDEAS

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    1. Zirbel, Craig L., 1997. "Translation and dispersion of mass by isotropic Brownian flows," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 1-29, October.
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