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Expansions and Contractions of Isotropic Stochastic Flows of Homeomorphisms

Vladimir V. Piterbarg
The Annals of Probability
Vol. 26, No. 2 (Apr., 1998), pp. 479-499
Stable URL: http://www.jstor.org/stable/2652820
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Expansions and Contractions of Isotropic Stochastic Flows of Homeomorphisms
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Abstract

A sequence of piecewise constant approximations to rescaled isotropic homeomorphic stochastic flows is shown to converge weakly in Skorohod metric to the coalescing Brownian flow. Intermittent behavior of isotropic flows is exposed, and the clustering properties of isotropic flows are studied by the means of this convergence. We obtain qualitative and quantitative description of expansions and contractions of an arbitrary isotropic homeomorphic flow on large time- and space-scales.

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