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Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

Author

Listed:
  • Anyue Chen

    (The University of Liverpool
    University of Hong Kong)

  • Phil Pollett

    (University of Queensland)

  • Junping Li

    (Central South University)

  • Hanjun Zhang

    (Xiangtan University)

Abstract

We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.

Suggested Citation

  • Anyue Chen & Phil Pollett & Junping Li & Hanjun Zhang, 2010. "Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 511-531, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-009-9121-y
    DOI: 10.1007/s11009-009-9121-y
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    References listed on IDEAS

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    1. Anyue Chen & Junping Li & N. I. Ramesh, 2005. "Uniqueness and Extinction of Weighted Markov Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 489-516, December.
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    Cited by:

    1. Anyue Chen & Junping Li & Jing Zhang, 2020. "Branching Collision Processes with Immigration," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1063-1088, September.

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