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Linear Expansion of Isotropic Brownian Flows


 
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1. Title Title of document Linear Expansion of Isotropic Brownian Flows
 
2. Creator Author's name, affiliation, country Michael Cranston; University of Rochester
 
2. Creator Author's name, affiliation, country Michael Scheutzow; Technische Universität Berlin
 
2. Creator Author's name, affiliation, country David Steinsaltz; University of California, Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic flows, Brownian flows, stochastic differentialequations, martingale fields, Lyapunov exponents
 
3. Subject Subject classification Primary: 60H20.
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-08-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1010
 
10. Identifier Digital Object Identifier 10.1214/ECP.v4-1010
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 4
 
12. Language English=en
 
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