{"title":"Perturbation analysis for continuous-time Markov chains in a weak sense","authors":"Na Lin, Yuanyuan Liu","doi":"10.1017/jpr.2024.20","DOIUrl":null,"url":null,"abstract":"By the technique of augmented truncations, we obtain the perturbation bounds on the distance of the finite-time state distributions of two continuous-time Markov chains (CTMCs) in a type of weaker norm than the <jats:italic>V</jats:italic>-norm. We derive the estimates for strongly and exponentially ergodic CTMCs. In particular, we apply these results to get the bounds for CTMCs satisfying Doeblin or stochastically monotone conditions. Some examples are presented to illustrate the limitation of the <jats:italic>V</jats:italic>-norm in perturbation analysis and to show the quality of the weak norm.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"41 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/jpr.2024.20","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
By the technique of augmented truncations, we obtain the perturbation bounds on the distance of the finite-time state distributions of two continuous-time Markov chains (CTMCs) in a type of weaker norm than the V-norm. We derive the estimates for strongly and exponentially ergodic CTMCs. In particular, we apply these results to get the bounds for CTMCs satisfying Doeblin or stochastically monotone conditions. Some examples are presented to illustrate the limitation of the V-norm in perturbation analysis and to show the quality of the weak norm.
通过增强截断技术，我们得到了两个连续时间马尔可夫链（CTMC）的有限时间状态分布距离的扰动边界，其规范类型比 V 规范更弱。我们推导了强遍历和指数遍历 CTMC 的估计值。特别是，我们应用这些结果得到了满足多布林或随机单调条件的 CTMC 的边界。我们列举了一些例子来说明 V 准则在扰动分析中的局限性，并展示了弱准则的质量。
期刊介绍：
Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used.
A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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