英文标题：
《Population viewpoint on Hawkes processes》
---
作者：
Alexandre Boumezoued
---
最新提交年份：
2015
---
英文摘要：
This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of linear Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.
---
中文摘要：
本文研究一类具有一般移民的线性Hawkes过程。这些是具有散粒噪声强度的计数过程，包括自激和外激模式。对于这些过程，我们引入了年龄金字塔的概念，它根据移民和出生而演变。这种结合了强度过程定义和分支表示的方法的优点是，人口年龄金字塔跟踪所有过去的事件。这是用来计算一类具有一般移民的线性Hawkes过程的新分布性质，它推广了流行的指数生育率函数。文中还给出了霍克斯过程及其基本种群的路径构造。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->