Deviation inequalities for a supercritical branching process in a random environment

Abstract

Let $\left\{Z_n,n\ge 0\right\}$ be a supercritical branching process in an independent and identically distributed random environment $\xi ={\left({\xi }_n\right)}_{n\ge 0}$. In this paper, we get some deviation inequalities for $\ln \left(Z_{n+n_0}/Z_{n_0}\right).$ And some applications are given for constructing confidence intervals.

References in corpus (2)

• Limit theorems for weakly subcritical branching processes in random environment
• Cramér large deviation expansions for martingales under Bernstein's condition