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1 results

  • Extinction Probability of Interacting Branching Collision Processes

  • Part of
  • Anyue Chen, Junping Li, Yiqing Chen, Dingxuan Zhou
  • Journal:
    Advances in Applied Probability / Volume 44 / Issue 1 / March 2012
    Published online by Cambridge University Press:
    04 January 2016, pp. 226-259
    Print publication:
    March 2012
    • Article
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  • We consider the uniqueness and extinction properties of the interacting branching collision process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process and a collision branching process. We establish that there is a unique IBCP, and derive necessary and sufficient conditions for it to be nonexplosive that are easily checked. Explicit expressions are obtained for the extinction probabilities for both regular and irregular cases. The associated expected hitting times are also considered. Examples are provided to illustrate our results.