Deviation inequalities for a supercritical branching process in a random environment

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