English

Large deviations for sums defined on a Galton-Watson process

Probability 2007-06-13 v1 Statistics Theory Statistics Theory

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].

Keywords

Cite

@article{arxiv.math/0605617,
  title  = {Large deviations for sums defined on a Galton-Watson process},
  author = {Klaus Fleischmann and Vitali Wachtel},
  journal= {arXiv preprint arXiv:math/0605617},
  year   = {2007}
}