The geometric rate of convergence of random iteration in the Hutchinson distance
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Using the Banach fixed-point theorem we provide a simple criterion of the geometric rate of convergence and of asymptotic stability of Markov operators in the Hutchinson distance. The obtained results are applied to sequences of iterates of random-valued functions.
KeywordsMarkov operators Random-valued functions Random iteration Asymptotic stability Rate of convergence
Mathematics Subject ClassificationPrimary 60J05 Secondary 37A99
This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education.
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