Linear Expansion of Isotropic Brownian Flows
Michael Cranston, University of Rochester
Michael Scheutzow, Technische Universität Berlin
David Steinsaltz, University of California, Berkeley
Abstract
We consider an isotropic Brownian flow on $R^d$ for $dgeq 2$ with
a positive Lyapunov exponent, and show that any nontrivial
connected set almost surely contains points whose distance from the
origin under the flow grows linearly with time. The speed is
bounded below by a fixed constant, which may be computed from the
covariance tensor of the flow. This complements earlier work, which
showed that stochastic flows with bounded local characteristics and
zero drift cannot grow at a linear rate faster than linear.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.