马尔可夫链次几何遍历性的等价条件及其在M/G/1排队中的应用
Equivalences of Subgeometric Ergodicity of Markov Chains and Its Application to M/G/1 Queue
DOI: 10.12677/aam.2025.145255, PDF,    科研立项经费支持
作者: 孟雨欣：西安电子科技大学数学与统计学院，陕西 西安；李文迪*：西安电子科技大学数学与统计学院，陕西 西安；湖南师范大学计算与随机数学教育部重点实验室，湖南 长沙
关键词: 马尔可夫链；次几何遍历；M/G/1嵌入排队过程；Markov Chain； Subgeometric Ergodicity； M/G/1 Embedded Queuing Process
摘要: 马尔可夫链的遍历性研究在随机过程理论中占有重要地位，本文聚焦于马尔可夫链的次几何遍历性，提出了次几何遍历的六个等价判定条件，这些等价条件对进一步探索一般马尔可夫过程的次几何遍历性提供了理论基础，并将其应用于排队论中经典的M/G/1嵌入过程，得到了易验证的M/G/1嵌入排队过程次几何遍历的判定条件。
Abstract: The study of the ergodicity of Markov chains holds a significant position in the theory of stochastic processes. This paper focuses on the subgeometric ergodicity of Markov chains and proposes six equivalent criteria for subgeometric ergodicity of Markov chains. These equivalent conditions provide a theoretical foundation for further exploration of the subgeometric ergodicity of general Markov processes. In addition, this paper applies these criteria to the classical M/G/1 embedded process in queueing theory, obtaining easily verifiable conditions for determining the subgeometric ergodicity of the M/G/1 embedded queueing process.
文章引用：孟雨欣, 李文迪. 马尔可夫链次几何遍历性的等价条件及其在M/G/1排队中的应用[J]. 应用数学进展, 2025, 14(5): 274-283. https://doi.org/10.12677/aam.2025.145255

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