Boundary measures of Markov chains

  title={Boundary measures of Markov chains},
  author={Elise E. Cawley and Brian Marcus and Selim Tuncel},
  journal={Israel Journal of Mathematics},
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… CONTINUE READING