Deviation inequalities for a supercritical branching process in a random environment

Abstract

Let {Z n , n ≥ 0} be a supercritical branching process in an independent and identically distributed random environment ξ = (ξ n ) n≥0 . In this paper, we get some deviation inequalities for ln (Z n+n 0 /Z n 0 ) . And some applications are given for constructing confidence intervals.