Can a higher-order Markov chain be treated as a first-order Markov chain?
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.
Fields of Study & Subjects
Advanced Queuing Theory Analysis
Markov Chains and Monte Carlo Methods
Petri Nets in System Modeling
Publication details
- Journal / source
- Probability in the Engineering and Informational Sciences
- Publisher
- Cambridge University Press (CUP)
- Volume
- 40
- Issue
- 3
- Pages
- 400–415
- Publication date
- 19 February 2026
- Language
- EN