Article contents
On large deviation rates for sums associated with Galton‒Watson processes
Published online by Cambridge University Press: 19 September 2016
Abstract
Given a supercritical Galton‒Watson process {Zn} and a positive sequence {εn}, we study the limiting behaviors of ℙ(SZn/Zn≥εn) with sums Sn of independent and identically distributed random variables Xi and m=𝔼[Z1]. We assume that we are in the Schröder case with 𝔼Z1 log Z1<∞ and X1 is in the domain of attraction of an α-stable law with 0<α<2. As a by-product, when Z1 is subexponentially distributed, we further obtain the convergence rate of Zn+1/Zn to m as n→∞.
Keywords
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Applied Probability Trust 2016
References
- 7
- Cited by