论文标题
谐波时刻和大偏差，用于关键的Galton-Watson过程
Harmonic moments and large deviations for a critical Galton-Watson process with immigration
论文作者
论文摘要
在本文中，研究了一个关键的Galton-Watson分支过程，其中包括移民$ z_ {n} $。我们首先获得$ z_ {n} $的谐波力矩的收敛速率。然后获得$ s_ {z_n}的大偏差：= \ sum_ {i = 1}^{z_n} x_i $，其中$ \ {x_i \} $是一系列独立且分布的零分布式零随机变量，带有尾巴index $α> 2 $。我们将看到融合率取决于移民平均值，繁殖的差异和$ x_1^+$的尾部指数，与超临界情况的先前结果相比，速率取决于Schröder常数和尾部指数。
In this paper, a critical Galton-Watson branching process with immigration $Z_{n}$ is studied. We first obtain the convergence rate of the harmonic moment of $Z_{n}$. Then the large deviation of $S_{Z_n}:=\sum_{i=1}^{Z_n} X_i$ is obtained, where $\{X_i\}$ is a sequence of independent and identically distributed zero-mean random variables with tail index $α>2$. We shall see that the converging rate is determined by the immigration mean, the variance of reproducing and the tail index of $X_1^+$, comparing to previous result for supercritical case, where the rate depends on the Schröder constant and the tail index.
