Large deviations for sums indexed by the generations of a Galton-Watson process

• 成果类型: Article
• 署名作者: Fleischmann, Klaus; Wachtel, Vitali
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Munich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0090-1
• 发表日期: 2008
• 页码: 445-470
• 关键词: branching-process; rates

摘要

In this paper, we study the large deviation behavior of sums SZ(n) of i.i.d. random variables X-i, where Z(n) is the nth generation of a supercritical Galton Watson process. We assume the finiteness of the moments EX12 and EZ(1)logZ(1). The underlying interplay of large deviation probabilities of partial sums of the X-i and of lower deviation probabilities of Z is clarified. Here, we heavily use lower deviation probability results on Z we recently published in [7].