论文标题
对随机环境中两个超临界分支过程的关键性参数的比较
Comparison on the criticality parameters for two supercritical branching processes in random environments
论文作者
论文摘要
令$ \ {z_ {1，n}，n \ geq 0 \} $和$ \ {z_ {2，n}，n \ geq 0 \} $是两个在不同随机环境中的两个超临界分支过程，具有关键性参数$μ_1$和$μ_2$。众所周知，$ \ frac {1} {n} \ ln z_ {1，n} \rightarrowμ_1$和$ \ frac {1} {1} {m} \ ln z_ {2，m}，m} \rightArrowμ_2$在可能的情况下是$，n \ m，frieftional of Implactiral contimention，n \ rightart \ frientar \ rightar \ fripery。 参数。为此，我们证明了一个非均匀的贝里 - 贝里（Berry-Esseen）的绑定和克拉米尔（Cramér）的中度偏差，以$ \ frac {1} {n} {n} \ ln z_ {1，n} - \ frac {1} {1} {m} {m} \ ln z__ {2，m} $ as $ m，n n \ m，n \ rifter and \ rifter fors for for for fors for for forty forty。 $μ_1-μ_2$。
Let $\{Z_{1,n} , n\geq 0\}$ and $\{Z_{2,n}, n\geq 0\}$ be two supercritical branching processes in different random environments, with criticality parameters $μ_1$ and $μ_2$ respectively. It is known that $\frac{1}{n} \ln Z_{1,n} \rightarrow μ_1$ and $\frac{1}{m} \ln Z_{2,m} \rightarrow μ_2$ in probability as $m, n \rightarrow \infty.$ In this paper, we are interested in the comparison on the two criticality parameters. To this end, we prove a non-uniform Berry-Esseen's bound and Cramér's moderate deviations for $\frac{1}{n} \ln Z_{1,n} - \frac{1}{m} \ln Z_{2,m}$ as $m, n \rightarrow \infty.$ An application is also given for constructing confidence interval for $μ_1-μ_2$.
