{"title":"The Multi-birth Property of Markov Branching Processes with Immigration","authors":"Yan-yun Li, Jun-ping Li","doi":"10.1007/s10255-026-0133-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the multi-birth property of Markov branching processes with immigration. The joint probability generating function of multi-birth numbers for Markov branching processes with immigration until time <i>t</i> is obtained by constructing a new <i>Q</i>-process. In particular, the probability generating function of multi-birth number is also obtained for Markov branching processes until its extinction.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1225 - 1244"},"PeriodicalIF":0.9000,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-026-0133-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we consider the multi-birth property of Markov branching processes with immigration. The joint probability generating function of multi-birth numbers for Markov branching processes with immigration until time t is obtained by constructing a new Q-process. In particular, the probability generating function of multi-birth number is also obtained for Markov branching processes until its extinction.
期刊介绍：
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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