论文标题
在随机环境中，均匀的cramér中度偏差和浆果 - 贝里 - 欧文界限
Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment
论文作者
论文摘要
令$ \ {z_n，n \ geq 0 \} $为独立且相同分布的随机环境中的超临界分支过程。我们证明了$ \ ln（z_ {z_ {n+n_0}/z_ {n_0}）$％％的cramér中度偏差和浆果 - 贝里 - 埃森的界限，在退火法下，在$ n_0 \ in \ mathbb {n} $中均匀地以GRAMA等人的相应结果为单位。 （随机过程。\appl。2017）以$ n_0 = 0 $建立。从理论上讲，该扩展很有趣，并且是由应用程序激励的。为证明开发了一种新方法； Grama等人的某些条件。 （2017）在我们目前的环境中放松。在构建置信区间时给出了一个应用程序的示例，以估算$ \ ln（z_ {n+n_0}/z__ {n_0}）$和$ n $的关键性参数。
Let $\{Z_n, n\geq 0\}$ be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate deviations and Berry-Esseen bounds for $\ln (Z_{n+n_0}/Z_{n_0})$ % under the annealed law, uniformly in $n_0 \in \mathbb{N}$, which extend the corresponding results by Grama et al. (Stochastic Process.\ Appl. 2017) established for $n_0=0$. The extension is interesting in theory, and is motivated by applications. A new method is developed for the proofs; some conditions of Grama et al. (2017) are relaxed in our present setting. An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of $\ln(Z_{n+n_0}/Z_{n_0})$ and $n$.
