Electronic Communications in Probability

Linear Expansion of Isotropic Brownian Flows

Michael Cranston, Michael Scheutzow, and David Steinsaltz

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Abstract

We consider an isotropic Brownian flow on $R^d$ for $d\geq 2$ 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.

Article information

Source
Electron. Commun. Probab., Volume 4 (1999), paper no. 12, 91-101.

Dates
Accepted: 27 August 1999
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456938434

Digital Object Identifier
doi:10.1214/ECP.v4-1010

Mathematical Reviews number (MathSciNet)
MR1741738

Zentralblatt MATH identifier
0938.60048

Subjects
Primary: 60H20: Stochastic integral equations

Keywords
Stochastic flows Brownian flows stochastic differentialequations martingale fields Lyapunov exponents

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Cranston, Michael; Scheutzow, Michael; Steinsaltz, David. Linear Expansion of Isotropic Brownian Flows. Electron. Commun. Probab. 4 (1999), paper no. 12, 91--101. doi:10.1214/ECP.v4-1010. https://projecteuclid.org/euclid.ecp/1456938434


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