Markovian Random Iterations of Maps

Edgar Matias

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arXiv · 1905.09981

Markovian Random Iterations of Maps

Edgar Matias

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Abstract

In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration, extending a similar classical result of independent and identically distributed random iterations. As an application, we prove a local synchronization property for Markovian random iterations of homeomorphisms of the circle $S^{1}$.

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Edgar Matias. 2019-05-24. Markovian Random Iterations of Maps. https://arxiv.org/abs/1905.09981

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