On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

[1] AMBROSIO, L.—GIGLI, N.: A user’s guide to optimal transport. In: Modelling and Optimisation of Flows on Networks, Lecture Notes in Math. Vol. 2062, Springer, Heidelberg, 2013, pp. 1–155.Search in Google Scholar

[2] BALÁŽ, V.—IACÒ, M. R.—STRAUCH, O.—THONHAUSER, S.—TICHY, R. F.: An extremal problem in uniform distribution theory, Unif. Distrib. Theory 11 (2016), no. 2. 1–21.Search in Google Scholar

[3] DURANTE, F.—SEMPI, C.: Principles of Copula Theory, CRC Press, Boca Raton, FL, 2016.10.1201/b18674Search in Google Scholar

[4] FIALOVÁ, J.—STRAUCH, O.: On two-dimensional sequences composed by one-dimensional uniformly distributed sequences, Unif. Distrib. Theory 6 (2011), no. 1. 101–125.Search in Google Scholar

[5] HOFER, M.—IACÒ, M. R.: Optimal bounds for integrals with respect to copulas and applications, J. Optim. Theory Appl. 161 (2014), no. 3, 999–1011.Search in Google Scholar

[6] IACÒ, M. R.—THONHAUSER, S.—TICHY, R. F.: Distribution functions, extremal limits and optimal transport, Indag. Math. (N.S.) 26 (2015), no. 5, 823–841.Search in Google Scholar

[7] KLEMENT, E. P.—KOLESÁROVÁ, A.—MESIAR, R.—SEMPI, C.: Copulas constructed from horizontal sections, Comm. Statist. Theory Methods 36 (2007), 2901–2911.10.1080/03610920701386976Search in Google Scholar

[8] MROZ, T.—TRUTSCHNIG, W.—FERNÁNDEZ SÁNCHEZ, J.: Distributions with fixed marginals maximizing the mass of the endograph of a function, 2016. arXiv:1602.05807,Search in Google Scholar

[9] NELSEN, R. B.: An Introduction to Copulas. 2nd edition. Springer Series in Statistics. Springer, New York, 2006.Search in Google Scholar

[10] PILLICHSHAMMER, F.—STEINERBERGER, S.: Average distance between consecutive points of uniformly distributed sequences. Unif. Distrib. Theory 4 (2009), no. 1, 51–67.Search in Google Scholar

[11] RACHEV, S. T.—RÜSCHENDORF, L.: Mass Transportation Problems. Vol. I. Theory. Probability and its Applications (New York). Springer-Verlag, New York, 1998.Search in Google Scholar

[12] RUDIN, W.: Real and Complex Analysis. 3rd ed. McGraw-Hill Book Co., New York, 1987.Search in Google Scholar

[13] RÜSCHENDORF, L.: Mathematical Risk Analysis. In: Springer Series in Operations Research and Financial Engineering. Springer, Heidelberg, 2013.10.1007/978-3-642-33590-7Search in Google Scholar

[14] SANTAMBROGIO, F.: Optimal Transport for Applied Mathematicians. Calculus of Variations, PDEs, and Modeling. In:Progress in Nonlinear Differential Equations and their Applications Vol. 87. Birkhäuser/Springer, Cham, 2015.10.1007/978-3-319-20828-2Search in Google Scholar

[15] STRAUCH, O.: Some applications of distribution functions of sequences, Unif. Distrib. Theory 10 (2015), no. 2, 117–183.Search in Google Scholar

[16] TRUTSCHNIG, W.: On a strong metric on the space of copulas and its induced dependence measure, J. Math. Anal. Appl. 384 (2011), 690–705.10.1016/j.jmaa.2011.06.013Search in Google Scholar