 Absorbing Markov and branching processes with instantaneous resurrectionAnthony G. Pakes Stochastic Processes and their Applications, 1993, vol. 48, issue 1, 85-106 Abstract: A Markov branching process with instantaneous immigration from the zero state can be constructed so as to be honest and have the non-negative integers as state-space, but the construction requires the branching part to be explosive. We show that a realistic model can be constructed without this restriction if the state-space is restricted to the natural numbers. Moreover this construction is the weak limit, in the sense of finite dimensional laws, of the Yamazato model as the zero state holding-time parameter tends to infinity. This idea of immediate resurrection from an absorbing subset is extended to any minimal discrete-state Markov process, and even to a larger class. Our emphasis is on existence and uniqueness of the transition functions of the resurrected process, and classification of its states. Keywords: branching; and; Markov; processes; transition; functions; and; generators; resurrection; recurrence; classification (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:48:y:1993:i:1:p:85-106 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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