Ivan Werner

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Certain discrete-time Markov processes on locally compact metric spaces which arise from graph-directed constructions of fractal sets with place-dependent probabilities are studied. Such systems naturally extend finite Markov chains and inherit some of their properties. It is shown that the Markov operator defined by such a system has a unique invariant(More)
The dynamically defined measures (DDMs) for invertible maps on an arbitrary set X are considered. A dynamically defined relative entropy measure ¯ K(Λ|φ0) is introduced. It is shown that it is a signed measure on the generated σ-algebra, which allows to obtain a lower bound for the DDM arising from an initial measure φ0 such that Λ ≪ φ0 and Λ is invariant(More)
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