On limiting probability distributions of higher order Markov chains

2025/06/10 by Lixing Han, Jianhong Xu, XU Jian-hong +2 · 2 citations
#Markov Chains and Monte Carlo Methods #Advanced Queuing Theory Analysis #Theoretical and Computational Physics

paper · pdf · doi:10.1080/03081087.2026.2646943

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.

Citations

• Markov chains with memory, tensor formulation, and the dynamics of power iteration
• Convergence of a second order Markov chain
• Factorization strategies for third-order tensors
• Tensor Decompositions and Applications

Cited by

• Can a higher-order Markov chain be treated as a first-order Markov chain?
• HOMC: A MATLAB Package for Higher Order Markov Chains

Related

• Full Randomness in the Higher Difference Structure of Two-state Markov Chains
• Can a higher-order Markov chain be treated as a first-order Markov chain?
• Accelerating Power Methods for Higher-order Markov Chains
• Stationary Probability Vectors of Higher-order Markov Chains
• Hidden tail chains and recurrence equations for dependence parameters\n associated with extremes of higher-order Markov chains