A general approach to branching processes in varying environment

Götz Kersting

Published 2017-03-06Version 1

Branching processes $(Z_n)_{n \ge 0}$ in varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results are general criteria for a.s. extinction and square-integrability of the martingale $(Z_n/\mathbf E[Z_n])_{n \ge 0}$ as well as Yaglom type result stating convergence in distribution of the suitably normalized population size $Z_n$, conditioned on the event $Z_n >0$.