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
We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate t...We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn展开更多
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.
文摘We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn
