Limit Theorems for Marked Hawkes Processes with Application to a Risk Model

被引：47

作者：

Karabash, Dmytro ^{[1
]}

Zhu, Lingjiong ^{[1
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

STOCHASTIC MODELS | 2015年 / 31卷 / 03期

关键词：

Hawkes processes; Central limit theorem; Large deviations; Self-exciting processes; Marked point processes; LARGE DEVIATIONS; PROBABILITIES;

D O I：

10.1080/15326349.2015.1024868

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This article focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with an example of application in finance.

引用

页码：433 / 451

页数：19

共 21 条

[1] Some limit theorems for Hawkes processes and application to financial statistics [J].