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October, 1986 Isotropic Stochastic Flows
Peter Baxendale, Theodore E. Harris
Ann. Probab. 14(4): 1155-1179 (October, 1986). DOI: 10.1214/aop/1176992360


We consider isotropic stochastic flows in a Euclidean space of $d$ dimensions, $d \geq 2$. The tendency of two-point distances and of tangent vectors to shrink or expand is related to the dimension and the proportion of the flow that is solenoidal or potential. Tangent vectors from the same point tend to become aligned in the same or opposite directions. The purely potential flows are characterized by an analogue of the curl-free property. Liapounov exponents are treated briefly. The rate of increase or decrease of the length of an arc of small diameter is related to the shape of the arc. In the case $d = 2$ a sufficient condition is given under which the length of a short arc has a high probability of approaching 0.


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Peter Baxendale. Theodore E. Harris. "Isotropic Stochastic Flows." Ann. Probab. 14 (4) 1155 - 1179, October, 1986.


Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0606.60014
MathSciNet: MR866340
Digital Object Identifier: 10.1214/aop/1176992360

Primary: 60B99
Secondary: 60G99

Keywords: flows of diffeomorphisms , Stochastic flows

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 4 • October, 1986
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