Isotropic stochastic flows: A survey. (English) Zbl 0751.60058

Diffusion processes and related problems in analysis, Vol. II: Stochastic flows, Proc. Conf. Charlotte/NC (USA) 1990, Prog. Probab. 27, 75-94 (1992).
[For the entire collection see Zbl 0742.00084.]
This article is a survey of some of the results on isotropic stochastic flows obtained during the last decade by Baxendale, Harris, Le Jan, Matsumoto, and the author. Contents include: 1. Covariances of \(d\)- dimensional isotropic random fields on \(\mathbb{R}^ d\). 2. How to construct the corresponding stochastic flows. 3. Coalescing and non-coalescing homogeneous stochastic flows on the line. 4. Isotropic stochastic flows in dimension \(d\geq 2\) with \(C^ 4\) covariance tensor. 5. Coalescing isotropic stochastic flows in dimensions 2 and 3.


60H20 Stochastic integral equations


Zbl 0742.00084