Can a higher-order Markov chain be treated as a first-order Markov chain?

2025/12/01 by Jianhong Xu, XU Jian-hong, Xu, Jianhong
Business, Management and Accounting · Computer Science · Mathematics · #Advanced Queuing Theory Analysis #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain mixing time #Markov kernel #Markov model #Markov property #Markov renewal process #Petri Nets in System Modeling #Variable-order Markov model

paper · pdf · open access · doi:10.1017/s0269964826100230

published in Probability in the Engineering and Informational Sciences 40(3), 1-16 (Cambridge University Press)

openalex created_date 2026/02/19 · openalex publication_date 2026/02/19 · openalex updated_date 2026/02/20

Abstract

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.

Citations

• On limiting probability distributions of higher order Markov chains
• Markov chains with memory, tensor formulation, and the dynamics of power iteration
• Convergence of a second order Markov chain
• Tensor Decompositions and Applications
• HOMC: A MATLAB Package for Higher Order Markov Chains

Cited by

• HOMC: A MATLAB Package for Higher Order Markov Chains

Related

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• HOMC: A MATLAB Package for Higher Order Markov Chains