{"title":"Markov Chains, Law of Total Probability, and Recurrence Relations","authors":"D. V. Vinogradov","doi":"10.3103/S0005105523010090","DOIUrl":null,"url":null,"abstract":"<p>The article describes a general method of estimating average hitting times and the associated probabilities for homogeneous finite Markov chains. Recurrence relations for the estimated values and probabilities are obtained using fundamental formulas of the law of total probability. The described method is applied to three problems of a coupled Markov chain of the VKF method; in each case, the resulting recurrence relations are solvable for exact solutions.</p>","PeriodicalId":42995,"journal":{"name":"AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0005105523010090","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The article describes a general method of estimating average hitting times and the associated probabilities for homogeneous finite Markov chains. Recurrence relations for the estimated values and probabilities are obtained using fundamental formulas of the law of total probability. The described method is applied to three problems of a coupled Markov chain of the VKF method; in each case, the resulting recurrence relations are solvable for exact solutions.
期刊介绍：
Automatic Documentation and Mathematical Linguistics is an international peer reviewed journal that covers all aspects of automation of information processes and systems, as well as algorithms and methods for automatic language analysis. Emphasis is on the practical applications of new technologies and techniques for information analysis and processing.
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