Deviation inequalities for a supercritical branching process in a random environment

Let $left { Z_{n}, nge 0 right }$ be a supercritical branching process in an independent and identically distributed random environment $xi =left ( xi _{n} right )_{ngeq 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.