Large deviations for sums defined on a Galton-Watson process
Klaus Fleischmann, Vitali Wachtel
Abstract
In 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 EX12 and EZ1log 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].
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