Tuero, Araceli On the stochastic convergence of representations based on Wasserstein metrics. (English) Zbl 0770.60012 Ann. Probab. 21, No. 1, 72-85 (1993). Under some regularity conditions an optimal coupling of two probability measures on a Hilbert space can be found in the form \((X,H(X))\) for some monotone function \(H\). It is shown that convergence of \(P_ n\) to \(P\) in distribution implies a.s. convergence of the optimal coupling functions \(H_ n\) in the finite-dimensional case. For the infinite-dimensional case a counterexample is given. Reviewer: L.Rüschendorf (Münster) Cited in 1 ReviewCited in 5 Documents MSC: 60E05 Probability distributions: general theory 60B10 Convergence of probability measures Keywords:stochastic convergence of representations; Skorokhod’s representation theorem; increasing functions; optimal coupling PDFBibTeX XMLCite \textit{A. Tuero}, Ann. Probab. 21, No. 1, 72--85 (1993; Zbl 0770.60012) Full Text: DOI