A unifying approach to branching processes in a varying environment

@article{Kersting2020AUA,
  title={A unifying approach to branching processes in a varying environment},
  author={G{\"o}tz Kersting},
  journal={Journal of Applied Probability},
  year={2020},
  volume={57},
  pages={196 - 220}
}
  • G. Kersting
  • Published 6 March 2017
  • Mathematics
  • Journal of Applied Probability
Abstract Branching processes $(Z_n)_{n \ge 0}$ in a varying environment generalize the Galton–Watson process, in that they allow time dependence of the offspring distribution. Our main results concern general criteria for almost sure extinction, square integrability of the martingale $(Z_n/\mathrm E[Z_n])_{n \ge 0}$, properties of the martingale limit W and a Yaglom-type result stating convergence to an exponential limit distribution of the suitably normalized population size $Z_n$, conditioned… 
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