Frobenius–Perron operator description of Markov chains

  1. Zbigniew S. Kowalski

Abstract

We consider canonical shift space representation of discretetime Markov chain given by transition kernels. Markov shifts and eigenfunctions of skew products above them are characterized by terms of Frobenius–Perron operator. The results are applied to the exactness property of Markov chains. We introduce also the notion of quasi-Markov chain and apply it to Gauss endomorphisms.

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Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 325 to 341

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