This article explores how higher-order Markov chains relate to first-order Markov chains, suggesting significant insights into their analysis.
It is well known that any higher-order Markov chain can be associated with a first-order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher-order and first-order Markov chains, together with illustrative examples. Our main objective is to address the central question as posed in the title.
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Jianhong Xu (2026) studied this question.
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