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 devi...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.展开更多
We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked...We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11371061）.
文摘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.
文摘We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.
