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On monotonically proceeding structures and stepwise increasing transition matrices of Markov chains

Journal Contribution - Journal Article

In general, the transition matrix of a Markov chain is a stochastic matrix. For a system that is modeled by a Markov chain, the transition matrix must reflect the characteristics of that system. The present paper introduces a particular class of transition matrices in order to model Markov systems for which, as the length of the time interval becomes greater, a transition from one state to another is more likely. We call these transition matrices stepwise increasing. Moreover in some contexts it is less desirable that the stocks fluctuate over time. In those situations, one is interested in monotonically proceeding stock vectors. This paper examines monotonically proceeding stock vectors and stepwise increasing transition matrices. We present conditions on the transition matrix such that all stock vectors are monotonically proceeding. In particular, the set of monotonically proceeding vectors is characterized for the two-state and three-state cases.
Journal: Communications in Statistics: Theory and Methods
ISSN: 0361-0926
Issue: 1
Volume: 51
Pages: 51 - 67
Publication year:2022
Keywords:Applied mathematics