带移民Jiina过程的弱极限定理

Weak Limit Theorems for Jiina Processes with Immigration

该文在矩条件下讨论了一列带移民Jiina过程的弱极限定理.按照极限过程的不同对矩条件作了简单分类.文章证明了在不同的矩条件下,一列带移民Jiina过程适当规范后可以在Skorokhod空间分别弱收敛到连续分支过程,带移民的连续分支过程,不连续的带移民分支过程以及确定性过程.对最后这种情形,还给出了一个波动极限定理.

The author studies the limit theorems of Jirina processes with immigration under moment conditions. The moment conditions are classified according to the limiting processes. It is proved that under different moment conditions, a sequence of scaled Jirina processes with immigration converges weakly in the Skorokhod space to the continuous branching process, the continuous branching process with immigration, the branching process with immigration with jumps and the deterministic process, respectively. For the last case, a fluctuation limit theorem is also proved.