Two dimensional probabilities with a given conditional structure

Štěpán, Josef ; Hlubinka, Daniel

Kybernetika, Tome 35 (1999) no. 3, p. [367].

Résumé

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].

Détail

Classification : 28A35, 60A10, 60B05, 60E05
Mots-clés : two-dimensional probabilities; extremal measure