Substitution Markov chains and Martin boundaries. (English) Zbl 1406.60112

Koslicki, David; Denker, Manfred

Rocky Mt. J. Math. 46, No. 6, 1963-1985 (2016).

Summary: Substitution Markov chains have been introduced [the first author, Substitution Markov chains with applications to molecular evolution. State College, PA: Pennsylvania State University (PhD Thesis) (2012)] as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although having a boundary homeomorphic to the well-known coin tossing process, has a metric description that differs significantly.

MSC:

60J50	Boundary theory for Markov processes
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
31C35	Martin boundary theory
37A50	Dynamical systems and their relations with probability theory and stochastic processes
28D05	Measure-preserving transformations

Keywords:

substitution Markov chain; Martin boundary; random substitution