Functional limit theorems for marked Hawkes point measures

被引：12

作者：

Horst, Ulrich ^{[1
,2
]}

Xu, Wei ^{[1
]}

机构：

[1] Humboldt Univ, Dept Math, Unter Linden 6, D-10099 Berlin, Germany

[2] Humboldt Univ, Sch Business & Econ, Unter Linden 6, D-10099 Berlin, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2021年 / 134卷

关键词：

Hawkes point measure; Marked Hawkes process; Functional limit theorem; Budding microbes in a host; CALORIC RESTRICTION; LARGE DEVIATIONS; SPECTRA; SENESCENCE; MODELS;

D O I：

10.1016/j.spa.2020.12.002

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 paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution by the sum of a Gaussian white noise process plus an appropriate lifting map of a correlated one-dimensional Brownian motion. The Brownian motion results from the self-exciting arrivals of events. We apply our limit theorems for Hawkes point measures to analyze the population dynamics of budding microbes in a host as well as their interaction with that host. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：94 / 131

页数：38

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