| Title:
|
Two dimensional probabilities with a given conditional structure (English) |
| Author:
|
Štěpán, Josef |
| Author:
|
Hlubinka, Daniel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
[367]-381 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A properly measurable set ${\cal P} \subset {X} \times M_1({Y})$ (where ${X}, {Y}$ are Polish spaces and $M_1(Y)$ is the space of Borel probability measures on $Y$) is considered. Given a probability distribution $\lambda \in M_1(X)$ the paper treats the problem of the existence of ${X}\times {Y}$-valued random vector $(\xi ,\eta )$ for which ${\cal L}(\xi )=\lambda $ and ${\cal L}(\eta | \xi =x) \in {\cal P}_x$ $\lambda $-almost surely that possesses moreover some other properties such as “${\cal L}(\xi ,\eta )$ has the maximal possible support” or “${\cal L}(\eta | \xi =x)$’s are extremal measures in ${\cal P}_x$’s”. The paper continues the research started in [7]. (English) |
| Keyword:
|
two-dimensional probabilities |
| Keyword:
|
extremal measure |
| MSC:
|
28A35 |
| MSC:
|
60A10 |
| MSC:
|
60B05 |
| MSC:
|
60E05 |
| idZBL:
|
Zbl 1274.60014 |
| idMR:
|
MR1704672 |
| . |
| Date available:
|
2009-09-24T19:26:24Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135293 |
| . |
| Reference:
|
[1] Aubin J.-P., Frankowska H.: Set Valued Analysis.Birkhäuser, Boston 1990 Zbl 1168.49014, MR 1048347 |
| Reference:
|
[2] Beneš V., (eds.) J. Štěpán: Distributions with Given Marginals and Moment Problems.Kluwer, Dordrecht 1997 Zbl 0885.00054, MR 1614650 |
| Reference:
|
[3] Cohn D. L.: Measure Theory.Birkhäuser, Boston 1980 Zbl 0860.28001, MR 0578344 |
| Reference:
|
[4] Kempermann J. H. B.: The general moment problem, a geometric approach.Ann. Math. Statist. 39 (1968), 93–122 MR 0247645, 10.1214/aoms/1177698508 |
| Reference:
|
[5] Meyer P. A.: Probability and Potentials.Blaisdell, Waltham 1966 Zbl 0271.60086, MR 0205288 |
| Reference:
|
[6] Schwarz L.: Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures.Oxford University Press, Oxford 1973 MR 0426084 |
| Reference:
|
[8] Winkler G.: Choquet Order and Simplices.(Lectures Notes in Mathematics 1145.) Springer–Verlag, Berlin 1985 Zbl 0578.46010, MR 0808401 |
| . |
