Another look at the finite mean supercritical Bienaymé–Galton–Watson process

Abstract

Let {Z n} be a finite mean supercritical Bienaymé– Galton–Watson process. It is known that there exist norming constants {C n} such that {Z n /C n} converges almost surely to a limit W. Also there is a whole literature concerning properties of {C n} and W. We attempt a new approach to the limit theory of {Z n} by relating it to the theory of sums of independent and identically distributed random variables.