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Recurrence of Markov branching processes with immigration

Author

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  • Chen, Anyue
  • Renshaw, Eric

Abstract

We derive criteria for assessing the recurrence and positive-recurrence of Markov branching processes with immigration. Although our method is designed to tackle the instantaneous immigration case investigated in Chen and Renshaw (1990), this new approach can also be applied to the stable immigration case previously considered by Yamazato (1975) and others.

Suggested Citation

  • Chen, Anyue & Renshaw, Eric, 1993. "Recurrence of Markov branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 231-242, April.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:2:p:231-242
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    Cited by:

    1. Anyue Chen, 2020. "Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2089-2118, December.
    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.
    3. Chen, Anyue & Renshaw, Eric, 1995. "Markov branching processes regulated by emigration and large immigration," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 339-359, June.

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