On optimal stationary couplings between stationary processes

Ludger Rüschendorf, Tomonari Sei

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


By a classical result of [10] the ρ{variant} 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 ρ{variant} distance in these cases in explicit form. We also extend the ρ{variant} distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary c-couplings. Our assumptions need in this case a geometric positive curvature condition.

Original languageEnglish
JournalElectronic Journal of Probability
Publication statusPublished - 2012
Externally publishedYes


  • Monge-Kantorovich theory
  • Optimal stationary couplings
  • Stationary processes
  • ρ{variant}-distance

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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