Large deviations from sums of negatively associated random variables indexed by a supercritica lGalton-Watson branching process

Large deviations from sums SZn∶=ΣZ n i=1 of negatively associated random variables with common distribution are studied, where Zn is the n-th generation of a supercritical Galton-Watson process. We improve upon previous results for sums of independently and identically distributed random variables by Fleischmann et al.