Inequalities for Ek(X,Y) when the marginals are fixed. (English) Zbl 0325.60002


60A05 Axioms; other general questions in probability
60E05 Probability distributions: general theory
Full Text: DOI


[1] Adams, C. R.; Clarkson, J. A., Properties of functions f(x,y) of bounded variation, Trans. Amer. Math. Soc., 36, 711-730 (1934) · JFM 60.0201.04
[2] Bártfai, P., über die Entfernung der Irrfahrtswege, Studia Sci. Math. Hungar., 5, 41-49 (1970) · Zbl 0274.60048
[3] Dall’Aglio, G., Sugli estremi dei momenti delle funzioni di ripartizione doppia, Ann. Sci. école Norm. Sup., 10, 35-74 (1956) · Zbl 0073.14002
[4] Dall’Aglio, G., Fréchet classes and compatibility of distribution functions, Symposia Mathematica 9, 131-150 (1972), New York: Academic Press, New York · Zbl 0243.60007
[5] Fréchet, M., Sur les tableaux de corrélation dont les marges sont données, Ann. Univ. Lyon, Sect. A, Sér., 3, 14, 53-77 (1951) · Zbl 0045.22905
[6] Hardy, G. H.; Littlewood, J. E.; Pólya, G., Inequalities (1952), Cambridge: Cambridge Univ. Press, Cambridge · Zbl 0047.05302
[7] Hobson, E. W., The Theory of Functions of a Real Variable and the Theory of Fourier’s Series (1950), Washington: Harren Press, Washington · JFM 38.0414.01
[8] Hoeffding, W., Ma\stabvariante Korrelationstheorie, Schr. Math. Inst. Univ. Berlin, 5, 181-233 (1940)
[9] Lehmann, E. L., Some concepts of dependence, Ann. Math. Statist., 37, 1137-1153 (1966) · Zbl 0146.40601
[10] Neumann, J. v., Functional Operators. Volume I: Measures and Integrals (1950), Princeton: Princeton Univ. Press, Princeton
[11] Pledger, G.; Proschan, F., Stochastic comparisons of random processes, with applications in reliability, J. Appl. Probability, 10, 572-585 (1973) · Zbl 0271.60097
[12] Skorokhod, A. V., Limit theorems for stochastic processes, Theor. Probability Appl., 1, 261-290 (1965)
[13] Tchen, A.H.T.: Exact inequalities for ∫Φ(x, y) dH(x, y) when H has given marginals. Manuscript (1975)
[14] Vallender, S. S., Calculation of the Wasserstein distance between probability distributions on the line, Theor. Probability Appl., 18, 784-786 (1973) · Zbl 0351.60009
[15] Veinott, A. F. Jr., Oprimal policy in a dynamic, single product, nonstationary inventory model with several demand classes, Operations Res., 13, 761-778 (1965) · Zbl 0143.21704
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.