Dispersion rates under finite mode Kolmogorov flows
type: Item
instance of: scholarly article
title: Dispersion rates under finite mode Kolmogorov flows
zbMATH Open document ID: 1021.60032
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: This paper extends results of the authors and the reviewer [Ann. Probab. 30, 2046-2080 (2002; Zbl 1017.60073), ibid. 28, 1852-1869 (2000) and Electron. Commun. Probab. 4, 91-101 (1999; Zbl 0938.60048)] on the expansion of sets under semimartingale flows, to the case of finite-mode approximations to Kolmogorov flows. Given a random compact starting set \(X\) with almost-sure positive volume, the result states that the maximum displacement of any point in \(X\) from the origin at time \(t\) grows linearly in \(t\), uniformly in all directions. That is, if \(\varphi(t,s,x)\) is the random mapping from time \(s\) to time \(t\), there are positive constants \(c\) and \(C\) such that \[ c\leq \inf_{u\in S^1} \liminf_{t\to\infty} t^{-1} \sup_{x\in X} \langle \varphi(t,0,x),u\rangle \leq \limsup_{t\to\infty} t^{-1} \sup_{x\in X} \|\varphi(t,0,x),u\|\leq C \] almost surely.
reviewed by: David Steinsaltz
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 76F55
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1906180
zbMATH Keywords: stochastic flow
zbMATH Keywords: dispersion
zbMATH Keywords: Kolmogorov flow
zbMATH Keywords: finite mode approximation
zbMATH Keywords: passive tracers
zbMATH Keywords: linear growth
zbMATH Keywords: velocity fields
author: Michael Craig Cranston
author: Michael Scheutzow
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1026915613
OpenAlex ID: W2065482627
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DOI: 10.1214/AOAP/1026915613
description: scientific article; zbMATH DE number 1906180