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Journals and Conferences
Certain discrete-time Markov processes on locally compact metric spaces which arise from graphdirected 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 measure (DDM) Φ arising from a finite measure φ0 on an initial σ-algebra on a set X and an invertible map acting on the latter is considered. Several lower bounds for it are obtained and sufficient conditions for its positivity are deduced under the general assumption that there exists an invariant measure Λ such that Λ ≪ φ0. In… (More)