| Title:
|
Implicit Markov kernels in probability theory (English) |
| Author:
|
Hlubinka, Daniel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
547-564 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Having Polish spaces $\Bbb X$, $\Bbb Y$ and $\Bbb Z$ we shall discuss the existence of an $\Bbb X \times \Bbb Y$-valued random vector $(\xi,\eta )$ such that its conditional distributions $\operatorname{K}_{x} = \Cal L(\eta\mid \xi=x)$ satisfy $e(x, \operatorname{K}_{x}) = c(x)$ or $e(x,\operatorname{K}_{x}) \in C(x)$ for some maps $e:\Bbb X\times \Cal M_1(\Bbb Y) \to \Bbb Z$, $c:\Bbb X \to \Bbb Z$ or multifunction $C:\Bbb X \to 2^{\Bbb Z}$ respectively. The problem is equivalent to the existence of universally measurable Markov kernel $\operatorname{K}:\Bbb X \to \Cal M_1(\Bbb Y)$ defined implicitly by $e(x, \operatorname{K}_{x}) = c(x)$ or $e(x,\operatorname{K}_{x}) \in C(x)$ respectively. In the paper we shall provide sufficient conditions for the existence of the desired Markov kernel. We shall discuss some special solutions of the $(e,c)$- or $(e,C)$-problem and illustrate the theory on the generalized moment problem. (English) |
| Keyword:
|
Markov kernels |
| Keyword:
|
universal measurability |
| Keyword:
|
selections |
| Keyword:
|
moment problems |
| Keyword:
|
extreme points |
| MSC:
|
28A35 |
| MSC:
|
28B20 |
| MSC:
|
46A55 |
| MSC:
|
60A10 |
| MSC:
|
60B05 |
| idZBL:
|
Zbl 1091.28003 |
| idMR:
|
MR1920531 |
| . |
| Date available:
|
2009-01-08T19:25:09Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119345 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| . |
