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Invariant Finitely Additive Measures for General Markov Chains and the Doeblin Condition
Mathematics, 2023 In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. Markov chains are given by a classical transition function that generates a pair of conjugate linear Markov operators in a Banach space of ...
Alexander Zhdanok
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Finitely Additive Equivalent Martingale Measures [PDF]
Journal of Theoretical Probability, 2010 Let $L$ be a linear space of real bounded random variables on the probability space $(Ω,\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\mathcal{A}$, such that $P\sim P_0$ and $E_P(X)=0$ for all $X\in L$, if and only if $c\,E_Q(X)\leq\text{ess sup}(-X)$, $X\in L$, for some constant $c>0$ and (countably additive) probability $Q ...
Patrizia Berti +2 more
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Decomposition of Finitely Additive Markov Chains in Discrete Space
Mathematics, 2022 In this study, we consider general Markov chains (MC) defined by a transition probability (kernel) that is finitely additive. These Markov chains were constructed by S. Ramakrishnan within the concepts and symbolism of game theory.
Alexander Zhdanok, Anna Khuruma
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Finitely additive measures on N
Topology and Its Applications, 1992 AbstractWe study finitely additive measures on N, in particular how nice such a measure can be. We would like our “nice” measures to satisfy the following demand: If Y is obtained from X by a process which makes sets r times as small, from an intuitive point of view, thenμ(Y)=r-1·μ(X) for all X, YϵP(N).
Eric K Van Douwen
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Quasi-Compactness of Operators for General Markov Chains and Finitely Additive Measures
MathematicsWe study Markov operators T, A, and T* of general Markov chains on an arbitrary measurable space. The operator, T, is defined on the Banach space of all bounded measurable functions.
Alexander Zhdanok
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On the Additive Property of Finitely Additive Measures [PDF]
Journal of Theoretical Probability, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Finitely Additive Vector Measures [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1970 In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.
James K Brooks
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Flows in Infinite-Dimensional Phase Space Equipped with a Finitely-Additive Invariant Measure
Mathematics, 2023 Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness of a measure is studied with respect to the group of shifts on a vector of Hilbert space, the ...
Vsevolod Zh. Sakbaev
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On projections of finitely additive measures [PDF]
Proceedings of the American Mathematical Society, 1979 A theorem of Z. Frolík and M. E. Rudin states that for every two-valued measure μ \mu
Jech, Thomas, Prikry, Karel
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A duality theoretic view on limits of finite structures: Extended version [PDF]
Logical Methods in Computer Science, 2022 A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of ...
Mai Gehrke, Tomáš Jakl, Luca Reggio
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