Displaying similar documents to “Irreducible Markov systems on Polish spaces”

On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský

Laurent Mazliak (2007)

Revue d'histoire des mathématiques

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We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.

Gibbs states for non-irreducible countable Markov shifts

Andrei E. Ghenciu, Mario Roy (2013)

Fundamenta Mathematicae

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We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts. ...

Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

Jeffrey J. Hunter (2016)

Special Matrices

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This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the...

Estimates for perturbations of discounted Markov chains on general spaces

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva (2003)

Applicationes Mathematicae

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We analyse a Markov chain and perturbations of the transition probability and the one-step cost function (possibly unbounded) defined on it. Under certain conditions, of Lyapunov and Harris type, we obtain new estimates of the effects of such perturbations via an index of perturbations, defined as the difference of the total expected discounted costs between the original Markov chain and the perturbed one. We provide an example which illustrates our analysis.

Simple Markov chains

O. Adelman (1976)

Annales scientifiques de l'Université de Clermont. Mathématiques

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Markov operators on the space of vector measures; coloured fractals

Karol Baron, Andrzej Lasota (1998)

Annales Polonici Mathematici

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We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.

Markov operators acting on Polish spaces

Tomasz Szarek (1997)

Annales Polonici Mathematici

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We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.

Conditional Markov chains - construction and properties

Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski (2015)

Banach Center Publications

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In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.

On a nonstandard approach to invariant measures for Markov operators

Andrzej Wiśnicki (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.

Why the Kemeny Time is a constant

Karl Gustafson, Jeffrey J. Hunter (2016)

Special Matrices

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We present a new fundamental intuition forwhy the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications.