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Two dimensional probabilities with a given conditional structure

Josef Štěpán, Daniel Hlubinka (1999)

Kybernetika

A properly measurable set 𝒫 X × 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 λ M 1 ( X ) the paper treats the problem of the existence of X × Y -valued random vector ( ξ , η ) for which ( ξ ) = λ and ( η | ξ = x ) 𝒫 x λ -almost surely that possesses moreover some other properties such as “ ( ξ , η ) has the maximal possible support” or “ ( η | ξ = x ) ’s are extremal...

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