Brian Marcus
IEEE Trans. Inf. Theory
It is known that each Markov chain has associated with it a polytope and a family of Markov measures indexed by the interior points of the polytope. Measure-preserving factor maps between Markov chains must preserve the associated families. In the present paper, we augment this structure by identifying measures corresponding to points on the boundary of the polytope. These measures are also preserved by factor maps. We examine the data they provide and give examples to illustrate the use of this data in ruling out the existence of factor maps between Markov chains.
Brian Marcus
IEEE Trans. Inf. Theory
Mike Boyle, Bruce Kitchens, et al.
Proceedings of the American Mathematical Society
Brian Marcus, Selim Tuncel
Ergodic Theory and Dynamical Systems
N.T. Sindhushayana, Brian Marcus, et al.
IMA Journal of Mathematical Control and Information