Deviation inequalities for a supercritical branching process in a random environment
Received:June 17, 2021  Revised:September 08, 2021
Key Word: Deviation inequalities   Branching processes   Random environment  
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慧义 许 Tianjin University 天津大学卫津路校区
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Abstract:
      Let {Zn, n ≥ 0} be a supercritical branching process in an independent and identically distributed random environment ξ = (ξn)n≥0. The statistical inference for the critical parameter μ = EX is an interesting research topic. In this paper, we get some deviation inequalities for statistical inference of μ, via the estimator ln (Zn+n0 /Zn0 ). Some applications are given for constructing confidence intervals of μ in terms of Zn+n0 /Zn0 and n, and estimating Zn+n0 in terms of Zn0 , μ and n.
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