Deviation Inequalities for a Supercritical Branching Process in a Random Environment
Received:June 17, 2021  Revised:October 17, 2021
Key Word: deviation inequalities   branching processes   random environment
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 Author Name Affiliation Huiyi XU Center for Applied Mathematics, Tianjin University, Tianjin 300072, P. R. China
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Let $\{Z_{n}, n\ge 0\}$ be a supercritical branching process in an independent and identically distributed random environment $\xi=(\xi _{n})_{n\geq 0}$. 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.