Asymptotic properties of supercritical branching processes I: The Galton-Watson process

Abstract

We obtain results connecting the distributions of the random variables Z 1 and W in the supercritical Galton-Watson process. For example, if a > 1, and converge or diverge together, and regular variation of the tail of one of Z 1 , W with non-integer exponent α > 1 is equivalent to regular variation of the tail of the other.