References
- [1] BALÁŽ, V.—MIŠÍK, L.—STRAUCH, O.—TÓTH, J. T.: Distribution functions of ratio sequences, III, Publ. Math. Debrecen 82 (2013), no. 3-4, 511-529.
- [2] _____ Distribution functions of ratio sequences, IV, Period. Math. Hungar. 66 (2013) no. 1, 1-22.
- [3] BEIGLBÖCK, M.—HENRY-LABORDÈRE, P.—PENKNER, F.: Model-independent bounds for option prices—a mass transport approach, Finance Stoch. 17 (2013), no. 3, 477-501.
- [4] BOSCH, W.: Functions that preserve the uniform distribution of sequences, Trans. Amer. Math. Soc. 307 (1988), no. 1, 143-152.
- [5| DRMOTA, M.—TICHY, R. F.: Sequences, Discrepancies and Applications, Lecture Notes in Mathematics Vol. 1651, Springer-Verlag, Berlin, 1997.
- [6] DURANTE, F.—SEMPI, C.: Principles of Copula Theory. CRC/Chapman & Hall, London, 2015.
- [7] FIALOVÁ, J.—STRAUCH, O.: On two-dimensional sequences composed by one-dimensional uniformly distributed sequences, Unif. Distrib. Theory 6 (2011), no. 1, 101–125.
- [8] GREKOS, G.—STRAUCH, O.: Distribution functions of ratio sequences. II, Unif. Distrib. Theory 2 (2007), no. 1, 53-77.
- [9] HOFER, M.—IACÒ, M. R.: Optimal bounds for integrals with respect to copulas and applications, Journal of Optimization Theory and Applications 161 (2014), no. 3, 999–1011.
- [10] IACÒ, M. R.—TICHY, R. F.—THONHAUSER, S.: Distribution functions, extremal limits and optimal transport. Preprint, 2015.
- [11] JAWORSKI, P.—DURANTE, F.—HÄRDLE, W.—RYCHLIK, T. (EDS.): Copula Theory and its Applications. In Proc. Lecture Notes in Statistics Vol. 198. Springer, Heidelberg, 2010.
- [12] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. In: Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974.
- [13] MCNEIL, A. J.—FREY, R.—EMBRECHTS, P.: Quantitative Risk Management. Princeton Series in Finance. (Concepts, techniques and tools) Princeton University Press, Princeton, NJ, 2005.
- [14] NELSEN, R. B.: An Introduction to Copulas, second edition. Springer Series in Statistics. Springer, New York, 2000.
- [15] PILLICHSHAMMER, F.—STEINERBERGER, S.: Average distance between consecutive points of uniformly distributed sequences, Unif. Distrib. Theory 4 (2009), no. 1, 51-67.
- [16] PORUBSKÝ, Š.—ŠALÁT, T.—STRAUCH, O.: Transformations that preserve uniform distribution, Acta Arith. 49 (1988), no. 5, 459-479.
- [17] PUCCETTI, G.—ÜSCHENDORF, L. R.: Sharp bounds for sums of dependent risks, J. Appl. Probab. 50 (2013), no. 1, 42-53.
- [18] ÜSCHENDORE, L. R.: Monge-Kantorovich transportation problem and optimal couplings, Jahresber. Deutsch. Math.-Verein. 109 (2007), no. 3, 113-137.
- [19] _____ Mathematical Risk Analysis. Springer Series in Operations Research and Financial Engineering. (Dependence, Risk Bounds, Optimal Allocations and Portfolios). Springer, Heidelberg, 2013.
- [20] ÜSCHENDORE, L. R.—UCKELMANN, L.: Numerical and analytical results for the transportation problem of Monge-Kantorovich, Metrika 51 (2000), no. 3, 245-258 (electronic).
- [21] STEINERBERGER, S.: Uniform distribution preserving mappings and variational problems, Unif. Distrib. Theory 4 (2009), no. 1, 117-145.
- [22] STRAUCH, O.—PORUBSKÝ, Š.: Distribution of Sequences: a Sampler, Schriftenreihe der Slowakischen Akademie der Wissenschaften Vol. 1, Series of the Slovak Academy of Sciences. Peter Lang, Frankfurt am Main, 2005.
- [23] STRAUCH, O.—TÓTH, J. T.: Distribution functions of ratio sequences, Publ. Math. Debrecen 58 (2001), no. 4, 751-778.
- [24] TICHY, R. F.—WINKLER, R.: Uniform distribution preserving mappings, Acta Arith. 60 (1991), no. 2. 177-18.
- [25] UCKELMANN, L.: Optimal couplings between one-dimensional distributions. In: Distributions with given marginals and moment problems (Prague, 1996), Kluwer Acad. Publ., Dordrecht, 1997, pp. 275-281.
- [26] VAN DER. CORPUT, J. G.: Verteilungsfunktionen I-II. Proc. Akad. Amsterdam 38 (1935), 813-821, 1058-1066.
- [27] _____ Verteilungsfunktionen III-VIII, Proc. Akad. Amsterdam 39 (1936), 10-19, 19-26, 149-153, 339-344, 489-494, 579-590.
- [28] VILLANI, C.: Optimal Transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] Vol. 338. Springer-Verlag, Berlin, 2009.
- [29] WEINSTOCK, R.: Calculus of Variations. Dover Publications, Inc., New York, 1974. (With applications to Physics and Engineering, Reprint of the 1952 edition.)