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Branching Collision Processes with Immigration

Author

Listed:
  • Anyue Chen

    (The Southern University of Science and Technology
    The University of Liverpool)

  • Junping Li

    (Central South University)

  • Jing Zhang

    (The Southern University of Science and Technology)

Abstract

We consider the regularity and ergodic properties of the Branching Collision Process with Immigration (BCIP) in this paper. We establish an easy checking sufficient condition under which the Feller minimal BCIP is honest. We provide some good conditions under which the Feller minimal BCIP is positive recurrent and then establish an analytic form of the generating function of the stationary distribution. The closely associated expected hitting times are also considered. Examples and numerical calculations are provided to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09745-1
    DOI: 10.1007/s11009-019-09745-1
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. Foucart, Clément & Vidmar, Matija, 2024. "Continuous-state branching processes with collisions: First passage times and duality," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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