This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Fleischmann, KlausWachtel, Vitali2016-03-242019-06-2820060946-8633https://doi.org/10.34657/2591https://oa.tib.eu/renate/handle/123456789/3057In this paper we study the large deviation behavior of sums of i.i.d. random variables Xi defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX2 1 and EZ1 log Z1 . The underlying interplay of the partial sums of the Xi and the lower deviation probabilities of Z is clarified. Here we heavily use lower deviation probability results on Z we recently published in [FW06].application/pdfeng510Large deviation probabilitiessupercritical Galton-Watson processeslower deviation probabilitiesSchröder caseBöttcher caseLotka-Nagaev estimatorReport