Two dimensional probabilities with a given conditional structure

Štěpán, Josef, and Hlubinka, Daniel. "Two dimensional probabilities with a given conditional structure." Kybernetika 35.3 (1999): [367]-381. <http://eudml.org/doc/33433>.

@article{Štěpán1999,
abstract = {A properly measurable set $\{\mathcal \{P\}\} \subset \{X\} \times M_1(\{Y\})$ (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 $\{\mathcal \{L\}\}(\xi )=\lambda $ and $\{\mathcal \{L\}\}(\eta | \xi =x) \in \{\mathcal \{P\}\}_x$$\lambda $-almost surely that possesses moreover some other properties such as “$\{\mathcal \{L\}\}(\xi ,\eta )$ has the maximal possible support” or “$\{\mathcal \{L\}\}(\eta | \xi =x)$’s are extremal measures in $\{\mathcal \{P\}\}_x$’s”. The paper continues the research started in [7].},
author = {Štěpán, Josef, Hlubinka, Daniel},
journal = {Kybernetika},
keywords = {two-dimensional probabilities; extremal measure; two-dimensional probabilities; extremal measure},
language = {eng},
number = {3},
pages = {[367]-381},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Two dimensional probabilities with a given conditional structure},
url = {http://eudml.org/doc/33433},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Štěpán, Josef
AU - Hlubinka, Daniel
TI - Two dimensional probabilities with a given conditional structure
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 3
SP - [367]
EP - 381
AB - A properly measurable set ${\mathcal {P}} \subset {X} \times M_1({Y})$ (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 ${\mathcal {L}}(\xi )=\lambda $ and ${\mathcal {L}}(\eta | \xi =x) \in {\mathcal {P}}_x$$\lambda $-almost surely that possesses moreover some other properties such as “${\mathcal {L}}(\xi ,\eta )$ has the maximal possible support” or “${\mathcal {L}}(\eta | \xi =x)$’s are extremal measures in ${\mathcal {P}}_x$’s”. The paper continues the research started in [7].
LA - eng
KW - two-dimensional probabilities; extremal measure; two-dimensional probabilities; extremal measure
UR - http://eudml.org/doc/33433
ER -