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On equal-input and monotone Markov matrices

Part of: Markov processes

Published online by Cambridge University Press:  06 June 2022

Michael Baake  and
Jeremy Sumner
Michael Baake*
Affiliation:
Bielefeld University
Jeremy Sumner*
Affiliation:
University of Tasmania
*
*Postal address: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany. Email: mbaake@math.uni-bielefeld.de
**Postal address: School of Natural Sciences, Discipline of Mathematics, University of Tasmania, Private Bag 37, Hobart, TAS 7001, Australia. Email: jeremy.sumner@utas.edu.au
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Abstract

The practically important classes of equal-input and of monotone Markov matrices are revisited, with special focus on embeddability, infinite divisibility, and mutual relations. Several uniqueness results for the classic Markov embedding problem are obtained in the process. To achieve our results, we need to employ various algebraic and geometric tools, including commutativity, permutation invariance, and convexity. Of particular relevance in several demarcation results are Markov matrices that are idempotents.

Keywords

Markov matrixembedding problemmonotone partial orderconvexity

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 460 - 492
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Copyright
© The Author(s) 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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