Banerjee, Sayan and Kendall, W. S. (2017) Rigidity for Markovian maximal couplings of elliptic diffusions. Probability Theory and Related Fields, 168 (1-2). pp. 55-112. doi:10.1007/s00440-016-0706-4 ISSN 0178-8051.

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Abstract

Maximal couplings are (probabilistic) couplings of Markov processes such that the tail probabilities of the coupling time attain the total variation lower bound (Aldous bound) uniformly for all time. Markovian (or immersion) couplings are couplings defined by strategies where neither process is allowed to look into the future of the other before making the next transition. Markovian couplings are typically easier to construct and analyze than general couplings, and play an important role in many branches of probability and analysis. Hsu and Sturm, in a preprint circulating in 2007, but later published in 2013, proved that the reflection-coupling of Brownian motion is the unique Markovian maximal coupling (MMC) of Brownian motions starting from two different points. Later, Kuwada (2009) proved that the existence of a MMC for Brownian motions on a Riemannian manifold enforces existence of a reflection structure on the manifold.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Homogeneous spaces , Large deviations , Riemannian manifolds, Stochastic differential equations
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer
ISSN:	0178-8051
Official Date:	June 2017
Dates:	Date Event June 2017 Published 13 April 2016 Available 28 March 2016 Accepted 8 December 2014 Submitted
Volume:	168
Number:	1-2
Page Range:	pp. 55-112
DOI:	10.1007/s00440-016-0706-4
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	11 April 2016
Date of first compliant Open Access:	11 August 2016
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/K013939
Open Access Version:	ArXiv

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