Convergence in L p and its exponential rate for a branching process in a random environment

@inproceedings{Huang2014ConvergenceIL,
  title={Convergence in L p and its exponential rate for a branching process in a random environment},
  author={Chunmao Huang and Quansheng Liu},
  year={2014}
}
We consider a supercritical branching process (Zn) in a random environment ξ. Let W be the limit of the normalized population size Wn = Zn/E[Zn|ξ]. We first show a necessary and sufficient condition for the quenched L (p > 1) convergence of (Wn), which completes the known result for the annealed L convergence. We then show that the convergence rate is exponential, and we find the maximal value of ρ > 1 such that ρ(W −Wn) → 0 in L, in both quenched and annealed sense. Similar results are also… CONTINUE READING

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