The Weak Irreducibility Markov Chains

Authors

  • Ren Zhang Primary Education College, Wuhan City Polytechnic, WuHan, China https://orcid.org/0000-0003-1750-5518
  • Shiling Zhao Primary Education College, Wuhan City Polytechnic, WuHan, China
  • Xia Wang Primary Education College, Wuhan City Polytechnic, WuHan, China
  • Kaijun Leng Research Center of Hubei Logistics Development, Hubei University of Economics, WuHan, China https://orcid.org/0000-0002-6962-2524

DOI:

https://doi.org/10.37256/cm.6420257270

Keywords:

weak irreducibility markov chains, times series analysis method, communicate, accessible, small set

Abstract

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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Published

2025-07-03

How to Cite

1.
Zhang R, Shiling Zhao, Xia Wang, Kaijun Leng. The Weak Irreducibility Markov Chains. Contemp. Math. [Internet]. 2025 Jul. 3 [cited 2025 Jul. 19];6(4):3976-90. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/7270