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Keywords:
marginal problem; marginal system; simplicial measure; set of marginal uniqueness
Summary:
The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.
References:
[1] Arnol'd V.I.: On functions of three variables (in Russian). Dokl. Akad. Nauk USSR 114 (1957), 679-681. MR 0111808
[2] Beneš V., Štěpán J.: The support of extremal probability measures with given marginals. In: Math. Stat. and Prob. Theory A (1987), 33-41. MR 0922685
[3] Beneš V., Štěpán J.: Extremal Solutions in the Marginal Problem. In: Advances in Probability Distributions with Given Marginals, Kluwer Academic Publishers, Dodrecht, 1991, 189-207. MR 1215952
[4] Douglas R.G.: On extremal measures and subspace density. Michigan Math. J. 11 (1964), 243-246. MR 0185427 | Zbl 0121.33102
[5] Dunford N., Schwartz J.T.: Linear Operators. Interscience Publishers Inc., New York, 1958. MR 0117523 | Zbl 0635.47003
[6] Ersov M.: The Choquet theorem and stochastic equations. Analysis Math. 1 (1975), 259-271. MR 0401995
[7] Hoffmann-Jørgensen J.: The general marginal problem. Lecture Notes in Math. 1242: Functional Analysis II, Springer-Verlag, 1987, 77-367. MR 0906272
[8] Kolmogorov A.N.: On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition (in Russian). Dokl. Akad. Nauk USSR 114 (1957), 953-956. MR 0111809
[9] Letac G.: Representation des mesures de probabilité sur le produit de deux espaces denombrables, de marges données. Ann. Inst. Fourier 16 (1966), 497-507. MR 0200957 | Zbl 0141.14801
[10] Štěpán J.: Simplicial Measures. In: Contributions to Statistics (J. Hájek Memorial Volume), Praha, 1977, 239-251. MR 0561272
[11] Štěpán J.: Probability Measures with Given Expectations. Proc. of the 2nd Prague Symp. on Asympt. Statistics, North Holland, 1979, 315-320. MR 0571198
[12] Štěpán J.: Weak Convergence in Probability Theory (in Czech). Charles University, Prague, 1988, Dr.\thinspace Sc. dissertation.
[13] Štěpán J.: Simplicial Measures and Sets of Uniqueness in Marginal Problem. Statistics and Decisions, 1991, to appear. MR 1257863
[14] Weizsäcker H. von, Winkler G.: Integral representation in the set of solutions of a generalized moment problem. Math. Ann. 246 (1979), 23-32. MR 0554129

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