Supercritical branching processes in random environments
Résumé
We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $\xi$, and present some recent results on the asymptotic properties of the limit variable $W$ of the natural martingale $W_n= Z_n/\mathbb{E}[Z_n|\xi]$, the convergence rates of $W - W_n $ (by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in $L^p$ and the convergence in probability), and limit theorems (such as central limit theorems, moderate and large deviations principles) on ($\log Z_n$).