Frobenius–Perron operator description of Markov chains
Słowa kluczowe:
Markov chain, quasi-Markov chain, exactness, Frobenius–Perron operator, measure-preserving transformation, skewproduct transformation, Gauss endomorphismAbstrakt
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.
