Remarks on the maxima of a martingale sequence with application to the simple critical branching process

Abstract

Let where {Zn, ℱn } is a non-negative submartingale satisfying Ei (Zn log Zn ) →∞. It is shown that When {Zn } is a simple critical Galton–Watson process and is slowly varying at∞, conditions are given ensuring that This gives an alternative proof of a result recently established by Kammerle and Schuh.