This paper reveals properties of limiting probability distributions in higher order markov chains, suggesting extended applicability of existing conditions.
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting probability distribution, including a sufficient condition for the existence of such a distribution. Our results extend the corresponding conclusions on first order chains. Besides, they complement the existing results concerning higher order chains which rely on approximation schemes or two-phase power iterations. Several illustrative example are also given.
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Han et al. (2025) studied this question.
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