Large deviations for sums defined on a Galton-Watson process

Details Large deviations for sums defined on a Galton-Watson process Large deviations for sums defined on a Galton-Watson process

2006-05-23

arxiv.org/abs/math/0605617v1

Mathematics

Probability

Scientific paper

In this paper we study the large deviation behavior of sums of i.i.d. random variables X_i defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX_1^2 and EZ_1log Z_1. The underlying interplay of the partial sums of the X_i 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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