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The survival probability of critical and subcritical branching processes in finite state space Markovian environment

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  • Grama, Ion
  • Lauvergnat, Ronan
  • Le Page, Émile

Abstract

Let (Zn)n≥0 be a branching process in a random environment defined by a Markov chain (Xn)n≥0 with values in a finite state space X. Let Pi be the probability law generated by the trajectories of Xnn≥0 starting at X0=i∈X. We study the asymptotic behaviour of the joint survival probability PiZn>0,Xn=j, j∈X as n→+∞ in the critical and strongly, intermediate and weakly subcritical cases.

Suggested Citation

  • Grama, Ion & Lauvergnat, Ronan & Le Page, Émile, 2019. "The survival probability of critical and subcritical branching processes in finite state space Markovian environment," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2485-2527.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2485-2527
    DOI: 10.1016/j.spa.2018.07.016
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    References listed on IDEAS

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    1. Dekking, F. M., 1987. "On the survival probability of a branching process in a finite state i.i.d. environment," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 151-157.
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