On Minimal Metrics in the Space of Random Variables

Previous article Next article On Minimal Metrics in the Space of Random VariablesA. SzulgaA. Szulgahttps://doi.org/10.1137/1127051PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. L. Dobrushin, Prescribing a system of random variables by conditional distributions, Theory Prob. Appl., 15 (1970), 458–486 0264.60037 LinkGoogle Scholar[2] R. M. Dudley, Probabilities and metrics, Matematisk Institut, Aarhus Universitet, Aarhus, 1976, 1–126, Lect. Notes, no. 45 58:7764 1014.62031 Google Scholar[3] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press Inc., New York, 1967xi+276 37:2271 0153.19101 CrossrefGoogle Scholar[4] V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist, 36 (1965), 423–439 31:1693 0135.18701 CrossrefGoogle Scholar[5] Alicja Szulga, On the Wasserstein metricTransactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, Reidel, Dordrecht, 1978, 267–273 81e:60003 0411.60016 Google Scholar[6] S. S. Vallender, Calculation of the Wasserstein distance between probability distributions on the line, Theory Prob. Appl., 18 (1973), 784–786 0351.60009 LinkGoogle Scholar[7] V. M. Zolotarev, Metric distances in spaces of random variables and of their distributions, Mat. Sb. (N.S.), 101(143) (1976), 416–454, 456, (In Russian.) 57:7720 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Robust Markov Decision Processes with Data-Driven, Distance-Based Ambiguity SetsSivaramakrishnan Ramani and Archis GhateSIAM Journal on Optimization, Vol. 32, No. 2 | 19 May 2022AbstractPDF (859 KB)Intertwinings and Stein’s magic factors for birth–death processesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 55, No. 1 | 1 Feb 2019 Cross Ref A Structural Classification of Probability DistancesThe Methods of Distances in the Theory of Probability and Statistics | 12 November 2012 Cross Ref On Choosing and Bounding Probability MetricsInternational Statistical Review, Vol. 70, No. 3 | 15 January 2007 Cross Ref Convergence of Laws on Separable Metric SpacesReal Analysis and Probability | 14 Oct 2002 Cross Ref A representation of the Kantorovich-FunctionalJournal of Theoretical Probability, Vol. 9, No. 1 | 1 Jan 1996 Cross Ref A general duality theorem for marginal problemsProbability Theory and Related Fields, Vol. 101, No. 3 | 1 Sep 1995 Cross Ref FréChet-Bounds and Their ApplicationsAdvances in Probability Distributions with Given Marginals | 1 Jan 1991 Cross Ref Nonlinear limit for a system of diffusing particles which alternate between two statesApplied Mathematics & Optimization, Vol. 22, No. 1 | 1 Jul 1990 Cross Ref System of interacting particles and nonlinear diffusion reflecting in a domain with sticky boundaryProbability Theory and Related Fields, Vol. 82, No. 2 | 1 Jun 1989 Cross Ref Poisson approximations in selected metrics by coupling and semigroup methods with applicationsJournal of Statistical Planning and Inference, Vol. 20, No. 1 | 1 Jan 1988 Cross Ref The Monge–Kantorovich Mass Transference Problem and Its Stochastic ApplicationsS. T. RachevTheory of Probability & Its Applications, Vol. 29, No. 4 | 17 July 2006AbstractPDF (2779 KB)Probability MetricsV. M. ZolotarevTheory of Probability & Its Applications, Vol. 28, No. 2 | 17 July 2006AbstractPDF (2381 KB) Volume 27, Issue 2| 1983Theory of Probability & Its Applications215-440 History Submitted:10 November 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127051Article page range:pp. 424-430ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics