A pedagogical unification of well‐known results on the limiting behaviour of Markov chains

Abstract

The traditional treatment of the limiting behaviour of Markov chains presents separate discussions and computational formulas for processes with irreducible recurrent periodic, irreducible recurrent aperiodic, and transient sets of states. This paper demonstrates how the limiting probabilities for all finite state space cases fall under the umbrella of one, generalized, computational result. In addition to the pedagogical value derived from conveying a simple probabilistic concept, this unification may prove insightful to researchers developing user‐friendly, computationally efficient computer programs concerned with the limiting behaviour of Markov chains. Such research could, in turn, promote growth in the practical application of Markov analysis as a modelling technique by increasing its accessibility to practitioners.