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Brownian couplings, convexity, and shy-ness


 
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1. Title Title of document Brownian couplings, convexity, and shy-ness
 
2. Creator Author's name, affiliation, country Wilfrid S. Kendall; University of Warwick
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, coupling
 
3. Subject Subject classification 60J65
 
4. Description Abstract Benjamini, Burdzy and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component processes of the coupling staying at least a given positive distance away from each other for all time. Among other results, they showed that no shy couplings could exist for reflected Brownian motions in $C^2$ bounded convex planar domains whose boundaries contain no line segments. Here we use potential-theoretic methods to extend this Benjamini et al.(2007) result (a) to all bounded convex domains (whether planar and smooth or not) whose boundaries contain no line segments, (b) to all bounded convex planar domains regardless of further conditions on the boundary.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-02-12
 
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/1417
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1417
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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