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Absorbing Markov and branching processes with instantaneous resurrection

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Publication Date
Volume
48
Issue
1
Identifiers
DOI: 10.1016/0304-4149(93)90108-g
Keywords
  • Branching And Markov Processes
  • Transition Functions And Generators
  • Resurrection
  • Recurrence Classification

Abstract

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.

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