On Limiting Probability Distributions of Higher Order Markov Chains
Probability
2026-03-20 v2 Statistics Theory
Statistics Theory
Abstract
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. 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.
Keywords
Cite
@article{arxiv.2506.08874,
title = {On Limiting Probability Distributions of Higher Order Markov Chains},
author = {Lixing Han and Jianhong Xu},
journal= {arXiv preprint arXiv:2506.08874},
year = {2026}
}