Rocky Mountain Journal of Mathematics

Substitution Markov chains and Martin boundaries

David Koslicki and Manfred Denker

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Abstract

Substitution Markov chains have been introduced \cite {KoslickiThesis2012} 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.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 1963-1985.

Dates
First available in Project Euclid: 4 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1483520434

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-1963

Mathematical Reviews number (MathSciNet)
MR3591268

Zentralblatt MATH identifier
06673139

Subjects
Primary: 28D05: Measure-preserving transformations 31C35: Martin boundary theory [See also 60J50] 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60J50: Boundary theory

Keywords
Substitution Markov chain Martin boundary random substitution

Citation

Koslicki, David; Denker, Manfred. Substitution Markov chains and Martin boundaries. Rocky Mountain J. Math. 46 (2016), no. 6, 1963--1985. doi:10.1216/RMJ-2016-46-6-1963. https://projecteuclid.org/euclid.rmjm/1483520434


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