摘要
我们与在文学为非移民盒子扩大以前的结果的移民 Z <sub> n </sub>, 为 supercritical 分叉过程学习泛音时刻的集中率。作为一个副产品，为 Z <sub> n+1 </sub>/Z <sub> n </sub> 的大偏差也被学习。我们能看到在集成取决于分叉和移民的产生功能的率有阶段转变。
We study the convergence rates of the harmonic moments for supercritical branching processes with immigration Zn, extending the previous results for non-immigration cases in literature. As a by-product, the large deviations for Zn＋1/Zn are also studied. We can see that there is a phase transition in converging rates depending on the generating functions of both branching and immigration.
基金
This work was supported by the National Natural Science Foundation of China （Grant No. 11371061）.
