Multiplicative functionals of dual processes

Ronald K. Getoor

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 $(X, ℬ, Φ, w)$ . We introduce the cone $𝔸$ of continuous additive functionals defined on $X$ and the cone $𝒫$ of regular potentials. We define an order relation “ $\leq$ ” 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 $\leq ℵ_{1}$ 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 $ℤ$ we shall discuss the existence of an $𝕏 \times 𝕐$ -valued random vector $(ξ, η)$ such that its conditional distributions $K_{x} = ℒ (η ∣ ξ = x)$ satisfy $e (x, K_{x}) = c (x)$ or $e (x, K_{x}) \in C (x)$ for some maps $e : 𝕏 \times ℳ_{1} (𝕐) \to ℤ$ , $c : 𝕏 \to ℤ$ or multifunction $C : 𝕏 \to 2^{ℤ}$ respectively. The problem is equivalent to the existence of universally measurable Markov kernel $K : 𝕏 \to ℳ_{1} (𝕐)$ defined implicitly by $e (x, K_{x}) = c (x)$ or $e (x, K_{x}) \in C (x)$ 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...

Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces

Angel Tamariz-Mascarúa, H. Villegas-Rodríguez (2002)

Commentationes Mathematicae Universitatis Carolinae

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A dense-in-itself space $X$ is called if the space of real continuous functions on $X$ with its box topology, $C_{□} (X)$ , is a discrete space. A space $X$ is called provided that $X$ is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with $κ$ -resolvable and almost resolvable spaces. We prove that every almost- $ω$ -resolvable space is $C_{□}$ -discrete, and that these classes coincide in the realm of completely...

Displaying similar documents to “Multiplicative functionals of dual processes”

Regular potentials of additive functionals in semidynamical systems

On ω -resolvable and almost- ω -resolvable spaces

Implicit Markov kernels in probability theory

Spaces of continuous functions, box products and almost- ω -resolvable spaces

On $ω$ -resolvable and almost- $ω$ -resolvable spaces

Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces