On limiting probability distributions of higher order Markov chains
Abstract
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behaviour. 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.
Fields of Study & Subjects
Data Mining Algorithms and Applications
Data Management and Algorithms
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Publisher
- Informa UK Limited
- Volume
- 74
- Issue
- 6
- Pages
- 740–756
- Publication date
- 19 March 2026
- Language
- EN