Normalizing constants for branching processes in random environments (B.P.R.E.)

AbstractNormalizing constants are obtained for B.P.R.E. such that the limiting random variable is finite almost everywhere and is zero only on the extinction set of the process w.p.1. Furthermore, the normalizing constants can be chosen so that they grow exponentially fast, and so that the ratio of successive constants converges in distribution. The method of proof used is to prove the result for increasing branching processes, and then, to transfer the result to general B.P.R.E. by employing the relationships between B.P.R.E., the associated B.P.R.E., and the reduced branching process