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Absorbing Markov and branching processes with instantaneous resurrection

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  • Pakes, Anthony G.

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.

Suggested Citation

  • Pakes, Anthony G., 1993. "Absorbing Markov and branching processes with instantaneous resurrection," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 85-106, October.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:1:p:85-106
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    Cited by:

    1. Wang, Juan & Li, Junping, 2013. "Uniqueness, recurrence and decay properties of collision branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1603-1612.
    2. Chen, Anyue & Renshaw, Eric, 2000. "Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 177-193, August.

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