Kendall, W. S. (2009) Brownian couplings, convexity, and shy-ness. Electronic communications in probability, Vol.14 (No.7). pp. 66-80. doi:10.1214/ECP.v14-1417 ISSN 1083-589X.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes
Journal or Publication Title:	Electronic communications in probability
Publisher:	University of Washington. Dept. of Mathematics
ISSN:	1083-589X
Official Date:	12 February 2009
Dates:	Date Event 12 February 2009 Published
Volume:	Vol.14
Number:	No.7
Number of Pages:	15
Page Range:	pp. 66-80
DOI:	10.1214/ECP.v14-1417
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	1 August 2016
Date of first compliant Open Access:	1 August 2016

Data sourced from Thomson Reuters' Web of Knowledge

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