Asymptotic properties of supercritical branching processes in random environments

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)/E[Z(n)vertical bar 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)).