Extremal solutions of a general marginal problem

Petra Linhartová

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 743-748
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Linhartová, Petra. "Extremal solutions of a general marginal problem." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 743-748. <http://eudml.org/doc/247315>.

@article{Linhartová1991,
abstract = {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.},
author = {Linhartová, Petra},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {marginal problem; marginal system; simplicial measure; set of marginal uniqueness; extreme point; marginal problem; marginal uniqueness; Hilbert's thirteenth problem},
language = {eng},
number = {4},
pages = {743-748},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extremal solutions of a general marginal problem},
url = {http://eudml.org/doc/247315},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Linhartová, Petra
TI - Extremal solutions of a general marginal problem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 743
EP - 748
AB - 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.
LA - eng
KW - marginal problem; marginal system; simplicial measure; set of marginal uniqueness; extreme point; marginal problem; marginal uniqueness; Hilbert's thirteenth problem
UR - http://eudml.org/doc/247315
ER -

References

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  2. Beneš V., Štěpán J., The support of extremal probability measures with given marginals, In: Math. Stat. and Prob. Theory A (1987), 33-41. (1987) MR0922685
  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. MR1215952
  4. Douglas R.G., On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246. (1964) Zbl0121.33102MR0185427
  5. Dunford N., Schwartz J.T., Linear Operators, Interscience Publishers Inc., New York, 1958. Zbl0635.47003MR0117523
  6. Ersov M., The Choquet theorem and stochastic equations, Analysis Math. 1 (1975), 259-271. (1975) MR0401995
  7. Hoffmann-Jørgensen J., The general marginal problem, Lecture Notes in Math. 1242: Functional Analysis II, Springer-Verlag, 1987, 77-367. MR0906272
  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. (1957) MR0111809
  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. (1966) Zbl0141.14801MR0200957
  10. Štěpán J., Simplicial Measures, In: Contributions to Statistics (J. Hájek Memorial Volume), Praha, 1977, 239-251. MR0561272
  11. Štěpán J., Probability Measures with Given Expectations, Proc. of the 2nd Prague Symp. on Asympt. Statistics, North Holland, 1979, 315-320. MR0571198
  12. Štěpán J., Weak Convergence in Probability Theory (in Czech), Charles University, Prague, 1988, Dr. Sc. dissertation. 
  13. Štěpán J., Simplicial Measures and Sets of Uniqueness in Marginal Problem, Statistics and Decisions, 1991, to appear. MR1257863
  14. Weizsäcker H. von, Winkler G., Integral representation in the set of solutions of a generalized moment problem, Math. Ann. 246 (1979), 23-32. (1979) MR0554129

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