Electronic Communications in Probability

Linear Expansion of Isotropic Brownian Flows

Michael Cranston, Michael Scheutzow, and David Steinsaltz

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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

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

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

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Zentralblatt MATH identifier

Primary: 60H20: Stochastic integral equations

Stochastic flows Brownian flows stochastic differentialequations martingale fields Lyapunov exponents

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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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