Boundary measures of Markov chains |
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Authors: | Elise Cawley Brian Marcus Selim Tuncel |
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Institution: | (1) Department of Mathematics, University of Chicago, 5734 University Avenue, 60637 Chicago, IL, USA;(2) IBM Almaden Research Center, K65/802, 650 Harry Road, 95120 San Jose, CA, USA;(3) Department of Mathematics, University of Washington, 98195 Seattle, WA, USA |
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Abstract: | 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.
E. Cawley was partially supported by the Modern Analysis joint NSF grant in Berkeley.
S. Tuncel was partially supported by NSF Grant DMS-9303240. |
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