Isotropic stochastic flows
type: Item
instance of: scholarly article
title: Isotropic stochastic flows
zbMATH Open document ID: 0606.60014
author: Peter H. Baxendale
author: Theodore E. Harris
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Various results on homogeneous isotropic stochastic flows in Euclidean space \({\mathbb{R}}^ d\) are gathered here. Being mainly formulated in terms of a decomposition of the flow into a potential (curl-free) and a solenoidal (divergence-free) part they include characterizations of the asymptotic behaviour of two point distances (which turns out to be different for \(d=2\), \(d=3\) or \(d\geq 4\), respectively) and of angle-length relations between pairs of tangent vectors - e.g., tangent vectors line up asymptotically, which is proved without explicitly using the fact that the two leading Lyapunov exponents are distinct. Further an analogue of the curl-free property is derived for potential isotropic flows and estimates of the lengths of arcs under the flow are given in dependence of their shapes. The paper concludes with a brief discussion of homogeneous nonisotropic flows.
Mathematics Subject Classification ID: 60B99
Mathematics Subject Classification ID: 60G99
zbMATH DE Number: 3980117
zbMATH Keywords: homogeneous isotropic stochastic flows
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: potential isotropic flows
zbMATH Keywords: homogeneous nonisotropic flows
reviewed by: Hans Crauel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992360
OpenAlex ID: W2049831275
DOI: 10.1214/AOP/1176992360
description: scientific article; zbMATH DE number 3980117