On a generalization of cyclic monotonicity and distances among random vectors
This paper is rather expository. It aims at characterizing solutions to the following problem. Let \(x\), \(y\) and \(z\) be \(R^ k\)-valued random vectors with given distributions. Which of the distributions on \(R^{3k}\) with these given distributions as margins will minimize \(E(| x-y|^ 2+| y-z|^ 2+| z-x|^ 2)\)?
scientific article; zbMATH DE number 566108