Large deviations for sums defined on a Galton-Watson process

Klaus Fleischmann; Vitali Wachtel

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Large deviations for sums defined on a Galton-Watson process

Klaus Fleischmann·Vitali Wachtel

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Abstract

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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BibTeX RIS

Klaus Fleischmann, Vitali Wachtel. 2006-05-23. Large deviations for sums defined on a Galton-Watson process. https://arxiv.org/abs/math/0605617

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