WIAS Preprint No. 1135, (2006)

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



Authors

  • Fleischmann, Klaus
  • Wachtel, Vitali

2010 Mathematics Subject Classification

  • 60J80 60F10

Keywords

  • Large deviation probabilities, supercritical Galton-Watson processes, lower deviation probabilities, Schröder case, Böttcher case, Lotka-Nagaev estimator

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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