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Displaying similar documents to “Multiplicative functionals of dual processes”

Regular potentials of additive functionals in semidynamical systems

Nedra Belhaj Rhouma, Mounir Bezzarga (2004)

Commentationes Mathematicae Universitatis Carolinae

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We consider a semidynamical system ( X , , Φ , w ) . We introduce the cone 𝔸 of continuous additive functionals defined on X and the cone 𝒫 of regular potentials. We define an order relation “ ” on 𝔸 and a specific order “ ” on 𝒫 . We will investigate the properties of 𝔸 and 𝒫 and we will establish the relationship between the two cones.

On ω -resolvable and almost- ω -resolvable spaces

J. Angoa, M. Ibarra, Angel Tamariz-Mascarúa (2008)

Commentationes Mathematicae Universitatis Carolinae

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We continue the study of almost- ω -resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, , Comment. Math. Univ. Carolin. (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded T 0 space with countable tightness and every T 1 space with π -weight 1 is hereditarily almost- ω -resolvable, (2) every crowded paracompact T 2 space which is the closed preimage of a crowded Fréchet T 2 space in such a way that the crowded part of each fiber is ω -resolvable, has this property...

Implicit Markov kernels in probability theory

Daniel Hlubinka (2002)

Commentationes Mathematicae Universitatis Carolinae

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Having Polish spaces 𝕏 , 𝕐 and we shall discuss the existence of an 𝕏 × 𝕐 -valued random vector ( ξ , η ) such that its conditional distributions K x = ( η ξ = x ) satisfy e ( x , K x ) = c ( x ) or e ( x , K x ) C ( x ) for some maps e : 𝕏 × 1 ( 𝕐 ) , c : 𝕏 or multifunction C : 𝕏 2 respectively. The problem is equivalent to the existence of universally measurable Markov kernel K : 𝕏 1 ( 𝕐 ) defined implicitly by e ( x , K x ) = c ( x ) or e ( x , K x ) 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...