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2012 On optimal stationary couplings between stationary processes
Ludger Rüschendorf, Tomonari Sei
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Electron. J. Probab. 17: 1-20 (2012). DOI: 10.1214/EJP.v17-1797


By a classical result of Gray, Neuhoff and Shields (1975) the rhobar-distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge--Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings which allow to calculate the rhobar distance in these cases in explicit form. We also extend the rhobar-distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary cbar-couplings. Our assumptions need in this case a geometric positive curvature condition.


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Ludger Rüschendorf. Tomonari Sei. "On optimal stationary couplings between stationary processes." Electron. J. Probab. 17 1 - 20, 2012.


Accepted: 28 February 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.60020
MathSciNet: MR2900458
Digital Object Identifier: 10.1214/EJP.v17-1797

Primary: 60E15
Secondary: 60G10

Keywords: $\bar\varrho$-distance , Monge--Kantorovich theory , Optimal stationary couplings , Stationary processes

Vol.17 • 2012
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