Let $\left(Z_n\right)$ be a supercritical branching process with immigration $\left(Y_n\right)$ in an independent and identically distributed environment $\xi .$ We consider the rate of convergence of the normalized population $W_n=Z_n/{\Pi }_n$ to its limit $W$, where $\left({\Pi }_n\right)$ is the usually used norming sequence, and establish a Berry–Esseen bound. Similar results are also obtained for $W_{n+k}-W_n$ for each fixed positive integer $k$.

中文翻译：

---

Berry-Esseen 在随机环境中的超临界分支过程与迁移

让$\left(Z_n\right)$成为具有移民的超临界分支过程$\left({\mathrm{是的}}_n\right)$在独立同分布的环境中$\xi .$我们考虑归一化总体的收敛速度$W_n=Z_n/{\Pi }_n$到极限$W$， 在哪里$\left({\Pi }_n\right)$是通常使用的规范序列，并建立 Berry-Esseen 界。也得到了类似的结果$W_{n+ķ}-W_n$对于每个固定的正整数$ķ$.