Work

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

Year: 2026

Type: article

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.

Source: Probability in the Engineering and Informational Sciences

DOI: 10.1017/s0269964826100230

Author: Jianhong Xu

Institution: Southern Illinois University Carbondale

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W4416968699