{"title":"Fluctuation Theory of Continuous-Time, Skip-Free Downward Markov Chains with Applications to Branching Processes with Immigration","authors":"Ronnie Loeffen, Pierre Patie, Jian Wang","doi":"10.1287/moor.2022.0246","DOIUrl":null,"url":null,"abstract":"We develop a comprehensive methodology for the fluctuation theory of continuous-time, skip-free Markov chains, extending and improving the recent work of Choi and Patie for discrete-time, skip-free Markov chains. As a significant application, we use it to derive a full set of fluctuation identities regarding exiting a finite or infinite interval for Markov branching processes with immigration, thereby uncovering many new results for this classic family of continuous-time Markov chains. The theory also allows us to recover in a simple manner fluctuation identities for skip-free downward compound Poisson processes.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"245 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of Operations Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1287/moor.2022.0246","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We develop a comprehensive methodology for the fluctuation theory of continuous-time, skip-free Markov chains, extending and improving the recent work of Choi and Patie for discrete-time, skip-free Markov chains. As a significant application, we use it to derive a full set of fluctuation identities regarding exiting a finite or infinite interval for Markov branching processes with immigration, thereby uncovering many new results for this classic family of continuous-time Markov chains. The theory also allows us to recover in a simple manner fluctuation identities for skip-free downward compound Poisson processes.
期刊介绍：
Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.
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