Stationary Probability Vectors of Higher-order Markov Chains
Chi-Kwong Li, Shixiao Zhang
TL;DR
This paper investigates the properties of higher-order Markov chains, characterizing those with universal stationary vectors and exploring the structure of their stationary set.
Contribution
It provides a characterization of second-order Markov chains that admit all probability vectors as stationary, and extends this to higher-order chains, analyzing their stationary set structure.
Findings
Characterization of second-order Markov chains with all probability vectors as stationary
Construction methods for higher-order Markov chains with the same property
Conditions determining the affine dimension of the stationary vector set
Abstract
We consider the higher-order Markov Chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same property. We also study conditions under which the set of stationary vectors of the Markov chain has a certain affine dimension.
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Taxonomy
TopicsTensor decomposition and applications · Matrix Theory and Algorithms · Markov Chains and Monte Carlo Methods