@article{EJP3388,
author = {Chunmao Huang and Quansheng Liu},
title = {Convergence in Lp and its exponential rate for a branching process in a random environment},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {branching process, varying environment, random environment, moments, exponential convergence rate, Lp convergence},
abstract = {We consider a supercritical branching process $(Z_n)$ in a random environment $\xi$. Let $W$ be the limit of the normalized population size $W_n=Z_n/\mathbb{E}[Z_n|\xi]$. We first show a necessary and sufficient condition for the quenched $L^p$ ($p>1$) convergence of $(W_n)$, which completes the known result for the annealed $L^p$ convergence. We then show that the convergence rate is exponential, and we find the maximal value of $\rho>1$ such that $\rho^n(W-W_n)\rightarrow 0$ in $L^p$, in both quenched and annealed sense. Similar results are also shown for a branching process in a varying environment.},
pages = {no. 104, 1-22},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3388},
url = {http://ejp.ejpecp.org/article/view/3388}}