Highly Influenced

# 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} }

- Published 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