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Displaying similar documents to “On the existence of invariant measures for Markov processes”

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.

The uniqueness of invariant measures for Markov operators

Tomasz Szarek (2008)

Studia Mathematica

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It is shown that Markov operators with equicontinuous dual operators which overlap supports have at most one invariant measure. In this way we extend the well known result proved for Markov operators with the strong Feller property by R. Z. Khas'minski.

Irreducible Markov systems on Polish spaces

Katarzyna Horbacz, Tomasz Szarek (2006)

Studia Mathematica

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Contractive Markov systems on Polish spaces which arise from graph directed constructions of iterated function systems with place dependent probabilities are considered. It is shown that their stability may be studied using the concentrating methods developed by the second author [Dissert. Math. 415 (2003)]. In this way Werner's results obtained in a locally compact case [J. London Math. Soc. 71 (2005)] are extended to a noncompact setting.

Invariant measures for random dynamical systems

Katarzyna Horbacz

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We consider random dynamical systems with randomly chosen jumps on Polish spaces. They generalize Markov processes corresponding to iterated function systems, Poisson driven stochastic differential equations, and irreducible Markov systems. We formulate criteria for the existence of an invariant measure and asymptotic stability for these systems. Estimates of the lower pointwise and concentration dimension of invariant measures are also given.