@article{89f498e3f9b14897b3536178d40ee335,
title = "Maximal Coupling of Euclidean Brownian Motions",
abstract = "We prove that the mirror coupling is the unique maximal Markovian coupling of two Euclidean Brownian motions starting from single points and discuss the connection between the uniqueness of maximal Markovian coupling of Brownian motions and certain mass transportation problems.",
keywords = "Euclidean Brownian motion, Maximal coupling, Mirror coupling",
author = "Hsu, {Elton P.} and Sturm, {Karl Theodor}",
note = "Funding Information: Acknowledgements We thank Pat Fitzsimmons and Wilfrid Kendall for their private communications on examples of maximal couplings which are not the mirror coupling. We also thank Mu-Fa Chen for his helpful comments. This research was supported in part by the NSF grant DMS-010479 and a Simons Foundation Collaboration Grant for Mathematicians (Hsu) and by the SFB 611 at the University of Bonn (Sturm). Publisher Copyright: {\textcopyright} 2013, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.",
year = "2013",
month = mar,
day = "1",
doi = "10.1007/s40304-013-0007-5",
language = "English (US)",
volume = "1",
pages = "93--104",
journal = "Communications in Mathematics and Statistics",
issn = "2194-6701",
publisher = "Springer Verlag",
number = "1",
}