A characterization of random variables with minimum L2-distance

L. Rüschendorf, S. T. Rachev

Research output: Contribution to journalArticlepeer-review

93 Scopus citations


A complete characterization of multivariate random variables with minimum L2 Wasserstein-distance is proved by means of duality theory and convex analysis. This characterization allows to determine explicitly the optimal couplings for several multivariate distributions. A partial solution of this problem has been found in recent papers by Knott and Smith.

Original languageEnglish
Pages (from-to)48-54
Number of pages7
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Jan 1990


  • L Wassertein-distance
  • marginals
  • optimal couplings
  • subgradients


Dive into the research topics of 'A characterization of random variables with minimum L2-distance'. Together they form a unique fingerprint.

Cite this