On a class of one-sided Markov shifts
Dynamical Systems
2007-05-23 v1 Probability
Abstract
We study one-sided Markov shifts, corresponding to positively recurrent Markov chains with countable (finite or infinite) state spaces. The following classification problem is considered: when two one-sided Markov shifts are isomorphic up to a measure preserving isomorphism In this paper we solve the problem for the class of rho-uniform (or finitely rho-Bernoulli) one-sided Markov shifts considered in Ru_6 We show that every ergodic rho-uniform Markov shift T can be represented in a canonical form T = T_G by means of a canonical (uniquely determined by T) stochastic graph G. In the canonical form, two such shifts T_{G_1} and T_{G_2} are isomorphic if and only if their canonical stochastic graphs G_1 and G_2 are isomorphic.
Keywords
Cite
@article{arxiv.math/0406059,
title = {On a class of one-sided Markov shifts},
author = {Ben-Zion Rubshtein},
journal= {arXiv preprint arXiv:math/0406059},
year = {2007}
}