Copulas

[1] AISLEITNER, CH.—HOFER, M.: On the limit distribution of consecutive elements of the van der Corput sequence, Unif. Distrib. Theory 8 (2013), no. 1, 89–96. Search in Google Scholar

[2] DE AMO, E.—CARRILLO, M. D.—J. FERNÁNDEZ-SÁNCHEZ, J.: Measure-preserving functions and the independence copula, Mediterr. J. Math. 8 (2011), 431–450. Search in Google Scholar

[3] BALAKRISHNAN, N.—CHIN-DIEW LAI: Continuous Bivariete Distributions. Second Edition, Springer Science + Businees Media, New York, 2009, DOI: 10.1007/b101765. Search in Google Scholar

[4] BALÁŽ, V.—FIALOVÁ, J.—GROZDANOV, V.—STOILOVA, S. —STRAUCH, O.: Hilbert space with reproducing kernel and uniform distribution preserving maps, I, Proc. Steklov Inst. Math. 282, (2013), Suppl. 1, S24–S53. Search in Google Scholar

[5] BALÁŽ, V.—FIALOVÁ, J.—HOFFER, M.—IACÓ, M. R. —STRAUCH, O.: The asymptotic distribution function of the 4-dimensional van der Corput sequence, Tatra Mt. Math. Publ. 64 (2015), 75–92 (Zbl 0654559.) Search in Google Scholar

[6] BALÁŽ, V.—IACÓ, 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, DOI:10.1515/udt-2016-0012. Search in Google Scholar

[7] BIRKHOFF, G.: Tres observaciones sobre el algebra lineal, Univ. Nac. Tucuman, Ser. A 5 (1946), 147–154. Search in Google Scholar

[8] O’CONNOR, J. J.—ROBERTSON, E. F.: Biography of Wassily Hoeffding. School of Mathematics and Statistics, University of St Andrews, Scotland, 2011. http://www-history.mcs.st-andrews.ac.uk/Biographies/Hoeffding.html Search in Google Scholar

[9] DARSOW, W. F.—NGUYEN, B.—OLSEN, E.T.: Copulas and Markov processes, Illinois J. Math. 36 (1996), no. 4, 600–642 Search in Google Scholar

[10] DRMOTA, M.—TICHY, R. F.: Sequences, Discrepancies and Applications. In: Lecture Notes in Mathematics Vol. 1651, Springer-Verlag, Berlin, Heidelberg, 1997. Search in Google Scholar

[11] FIALOVÁ, J.—MIŠÍK, L.—STRAUCH, O.: An asymptotic distribution functions of the three-dimensional shifted van der Corput sequence, Applied Mathematics, 5 (2014), Suppl. 1, 2334–2359, http://dx.doi.org/10.4236/am.2014.515227 Search in Google Scholar

[12] HELLEKALEK, P.—NIEDERREITER, H.: Construction of uniformly distributed sequences using the b-adic method, Unif. Distrib. Theory 6 (2011) no. 1, 185–200. Search in Google Scholar

[13] HOFER, M.—IACÒ, M. R.: Optimal bounds for integrals with respect to copulas and applications, J. Optim. Theory Appl. 161 (2014), no. 3, DOI:10.1007/s10957-013-0454-x. Search in Google Scholar

[14] HOFER, R.—KRITZER, P.—LARCHER, G.—PILLICHSHAMMER, F.: Distribution properties of generalized van der Corput-Halton sequences and their subsequence Int. J. Number Theory 5 (2009), 719–746. Search in Google Scholar

[15] JAWORSKI, P.—DURANTE, F.—HÄRDLE, W.—RYCHLIK, T.: Copula Theory and Its Applications, Proceedings of the Workshop Held in Warsaw, 25–26 September 2009, Lecture Notes in Statistics—Proceedings Vol. 198 Springer-Verlag, Berlin, 2010, DOI: 10.1007/978-3-642-12465-5. Search in Google Scholar

[16] JOE, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London, 1997. Search in Google Scholar

[17] MOLNÁR, S. H.: Sequences and their transforms with identical asymptotic distribution function, Studia Sci. Math. Hungar. 29 (1994), no. 3–4, 315–322. Search in Google Scholar

[18] NELSEN, R. B.: An Introduction to Copulas. Properties and Applications, Lecture Notes in Statistics Vol. 139 Springer-Verlag, New York, 1999. (Second edition, 2005). Search in Google Scholar

[19] NEWCOMB, S.: Note on the frequency of use of the different digits in natural numbers,Amer. J. Math. 4 (1881), 39–41, (JFM 13.0161.01). Search in Google Scholar

[20] OVERBECK, L.—SCHMIDT, W. M.: Multivariete Markov families of copulas, Dependence Modeling 3 (2015), no. 1, DOI: 10.1515/demo-2015-0011. Search in Google Scholar

[21] PAŠTÉKA, M.: On distribution functions of sequences, Acta Math. Univ. Come-nian. 50–51 (1987), 227–235 (MR 90c:11115). Search in Google Scholar

[22] 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

[23] PORUBSKÝ,Š.—ŠALÁT, T.—STRAUCH, O.: On a class of uniform distributed sequences, Math. Slovaca 40 (1990), 143–170 (MR 92d:11076). Search in Google Scholar

[24] RIVKIND, JA. I.: Problems in Mathematical Analysis, 2nd edition, Izd. Vyšejšaja škola, Minsk, (1973). (In Russian) Search in Google Scholar

[25] SCHATTE, P.: On transformations of distribution functions on the unit interval– –a generalization of the Gauss-Kuzmin-Lévy theorem, Z. Anal. Anwendungen 12 (1993), 273–283. Search in Google Scholar

[26] SCHMELING, J.—WINKLER, R.: Typical dimension of the graph of certain functions, Monatsh. Math. 119 (1995), 303–320 (MR 96c:28005). Search in Google Scholar

[27] SKLAR, M.: Fonctions de répartitionà n dimensions et leurs marges, Publ. Inst. Statis. Univ. Paris 8 (1959), 229–231 (MR 23# A2899). Search in Google Scholar

[28] STEINERBERGER, S.: Uniform distribution preserving mappings and variational problems, Unif. Distrib. Theory 4 (2009), no. 1, 117–145. Search in Google Scholar

[29] STEINERBERGER, S.: Extremal uniform distribution and random chord,Acta Math. Hungar. 130 (2011), no. 4, 321–339 Search in Google Scholar

[30] STRAUCH, O.: L² discrepancy, Math. Slovaca 44 (1994), 601–632. Search in Google Scholar

[31] STRAUCH, O.: On set of distribution functions of a sequence,in: Proc. Conf. Analytic and Elementary Number Theory, In Honor of E. Hlawka’s 80th Birthday, Vienna, July 18-20, 1996, Universit¨at Wien and Universit¨at für Bodenkultur, (W. G. Nowak and J. Schoißengeier, eds.) Vienna, 1997, 214–229 (Zbl 886.11044). Search in Google Scholar

[32] STRAUCH, O.: Unsolved Problems, Tatra Mt. Math. Publ. 56 (2013), 109–229, DOI: 10.2478/tmmp-2013-002; Electronic version: Unsolved Problems, Section on the homepage of Uniform Distribution Theory, http://pcwww.liv.ac.uk//~karpenk/JournalUDT/welcome-Dateien/unsolvedproblems.pdf Search in Google Scholar

[33] STRAUCH, O.: Distribution of Sequences Doctor Thesis, Mathematical Institute of the Slovak Academy of Sciences, Bratislava, Slovakia, 1999. (In Slovak), Search in Google Scholar

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

[35] STRAUCH, O.: Distribution of Sequences: A Theory, VEDA, Bratislava, 2019, ISBN 978-80-224-1734-1. Academia, Prague, 2019, ISBN 978-80-200-3010-8, pp. 592. Search in Google Scholar

[36] STRAUCH, O.—PORUBSKÝ,Š. : Distribution of Sequences: A Sampler, Peter Lang, Frankfurt am Main, 2005. Electronic revised version January 22, 2017, pp. 690, https://math.boku.ac.at/udt Search in Google Scholar

[37] STRAUCH, O.—TÓTH, J. T.: Distribution functions of ratio sequences, Publ. Math. Debrecen 58 (2001), no. 4, 751–778. Search in Google Scholar

[38] SUN, Y.: Some properties of uniform distributed sequences,J.NumberTheory 44 (1993), no. 3, 273–280 (MR 94h:11068). Search in Google Scholar

[39] SUN, Y.: Isomorphisms for convergence structures,Adv.Math. 116 (1995), no. 2, 322–355 (MR 97c:28031). Search in Google Scholar

[40] TICHY, R. F.—WINKLER, R.: Uniform distribution preserving mappings, Acta Arith. 60 (1991), no. 2, 177–189 (MR 93c:11054). Search in Google Scholar

[41] WINKLER, R.: On the distribution behaviour of sequences,Math. Nachr. 186 (1997), 303–312. Search in Google Scholar