| Title:
|
Extremal solutions of a general marginal problem (English) |
| Author:
|
Linhartová, Petra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
743-748 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
marginal problem |
| Keyword:
|
marginal system |
| Keyword:
|
simplicial measure |
| Keyword:
|
set of marginal uniqueness |
| MSC:
|
28A33 |
| MSC:
|
46A55 |
| MSC:
|
46N30 |
| MSC:
|
52A05 |
| MSC:
|
60B05 |
| idZBL:
|
Zbl 0751.60006 |
| idMR:
|
MR1159821 |
| . |
| Date available:
|
2009-01-08T17:48:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118454 |
| . |
| Reference:
|
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| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[4] Douglas R.G.: On extremal measures and subspace density.Michigan Math. J. 11 (1964), 243-246. Zbl 0121.33102, MR 0185427 |
| Reference:
|
[5] Dunford N., Schwartz J.T.: Linear Operators.Interscience Publishers Inc., New York, 1958. Zbl 0635.47003, MR 0117523 |
| Reference:
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[6] Ersov M.: The Choquet theorem and stochastic equations.Analysis Math. 1 (1975), 259-271. MR 0401995 |
| Reference:
|
[7] Hoffmann-Jørgensen J.: The general marginal problem.Lecture Notes in Math. 1242: Functional Analysis II, Springer-Verlag, 1987, 77-367. MR 0906272 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0141.14801, MR 0200957 |
| Reference:
|
[10] Štěpán J.: Simplicial Measures.In: Contributions to Statistics (J. Hájek Memorial Volume), Praha, 1977, 239-251. MR 0561272 |
| Reference:
|
[11] Štěpán J.: Probability Measures with Given Expectations.Proc. of the 2nd Prague Symp. on Asympt. Statistics, North Holland, 1979, 315-320. MR 0571198 |
| Reference:
|
[12] Štěpán J.: Weak Convergence in Probability Theory (in Czech).Charles University, Prague, 1988, Dr.\thinspace Sc. dissertation. |
| Reference:
|
[13] Štěpán J.: Simplicial Measures and Sets of Uniqueness in Marginal Problem.Statistics and Decisions, 1991, to appear. MR 1257863 |
| Reference:
|
[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 |
| . |
