发表机构
Escuela Superior Politécnica del Litoral（厄瓜多尔高等理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将典范拓扑与离散时间马尔可夫链的转移算子关联，定义了马尔可夫可达拓扑，建立了概率可达性与序理论拓扑的联系，还刻画了吸收子集等概念并研究了通信商与可 lump 性的关系。
AI 中文摘要
本文将典范拓扑与离散时间马尔可夫链的转移算子相关联，证明该构造定义了一种称为马尔可夫可达拓扑的亚历山德罗夫拓扑，随后确定其与可达关系诱导的亚历山德罗夫拓扑一致，建立了概率可达性与序理论拓扑之间的直接联系，使马尔可夫链理论的若干经典概念可从拓扑角度解读。除其他结果外，本文将吸收子集刻画为闭集，将不可约性与拓扑连通性及拓扑的平凡性关联，通过可达性和击中概率描述极小开邻域，并研究通信商及其与 lumpability（可 lump 性）的关系。
英文摘要
In this paper, we associate a canonical topology with the transition operator of a discrete-time Markov chain. We prove that this construction defines an Alexandroff topology, called the Markov Accessibility Topology, and subsequently establish that it coincides with the Alexandroff topology induced by the accessibility relation. This establishes a direct connection between probabilistic accessibility and order-theoretic topology, allowing several classical notions from Markov chain theory to be interpreted in topological terms. Among other results, we characterize absorbing subsets as closed sets, relate irreducibility to topological connectedness and the triviality of the topology, describe minimal open neighborhoods through accessibility and hitting probabilities, and investigate the communication quotient together with its relationship to lumpability.
Comments20 pages
