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$$\lambda $-almost surely that possesses moreover some other properties such as “${\cal L}(\xi ,\eta )$ has the maximal possible support” or “${\cal L}(\eta | \xi =x)$’s are extremal measures in ${\cal P}_x$’s”. The paper continues the research started in [7].
A properly measurable set ${\cal P} \subset {X} \times M_1({Y})$ (where ${X}, {Y}$ are Polish spaces and $M_1(Y)$ is the space of Borel probability measures on $Y$) is considered. Given a probability distribution $\lambda \in M_1(X)$ the paper treats the problem of the existence of ${X}\times {Y}$-valued random vector $(\xi ,\eta )$ for which ${\cal L}(\xi )=\lambda $ and ${\cal L}(\eta | \xi =x) \in {\cal P}_x$$\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].
@article{KYB_1999_35_3_a5,
author = {\v{S}t\v{e}p\'an, Josef and Hlubinka, Daniel},
title = {Two dimensional probabilities with a given conditional structure},
journal = {Kybernetika},
pages = {367--381},
year = {1999},
volume = {35},
number = {3},
mrnumber = {1704672},
zbl = {1274.60014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/}
}
TY - JOUR
AU - Štěpán, Josef
AU - Hlubinka, Daniel
TI - Two dimensional probabilities with a given conditional structure
JO - Kybernetika
PY - 1999
SP - 367
EP - 381
VL - 35
IS - 3
UR - http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/
LA - en
ID - KYB_1999_35_3_a5
ER -
%0 Journal Article
%A Štěpán, Josef
%A Hlubinka, Daniel
%T Two dimensional probabilities with a given conditional structure
%J Kybernetika
%D 1999
%P 367-381
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/
%G en
%F KYB_1999_35_3_a5
Štěpán, Josef; Hlubinka, Daniel. Two dimensional probabilities with a given conditional structure. Kybernetika, Tome 35 (1999) no. 3, pp. 367-381. http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/
