The Weak Irreducibility Markov Chains
DOI:
https://doi.org/10.37256/cm.6420257270Keywords:
weak irreducibility markov chains, times series analysis method, communicate, accessible, small setAbstract
Irreducibility serves as the foundational concept in the theoretical study of Markov chains. This paper introduces a generalized notion termed weak irreducibility and investigates its stochastic stability properties for Markov chains defined on countable state spaces. We establish the existence of invariant measures and stationary distributions for weak irreducibility Markov chains and provide an illustrative example demonstrating its practical relevance. Moreover, we extend the framework of weak irreducibility to general state spaces without requiring the prior assumptions of separability and the existence of a reference measure.
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Copyright (c) 2025 Ren Zhang, Shiling Zhao, Xia Wang, Kaijun Leng

This work is licensed under a Creative Commons Attribution 4.0 International License.