On equal-input and monotone Markov matrices. (June 2022)

• Record Type: Journal Article
• Authors: Baake, Michael; Sumner, Jeremy
• Is Part Of: Advances in applied probability. Volume 54:Number 2(2022)
• Page Start: 460
• Page End: 492
• Publication Date: 2022-06
• Subjects: Markov matrix -- embedding problem -- monotone partial order -- convexity; 60J10; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2021.39
• Languages: English
• ISSNs: 0001-8678

Abstract

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.