Asymptotic analysis of Poisson shot noise processes, and applications

被引：2

作者：

Torrisi, Giovanni Luca ^{[1
]}

Leonardi, Emilio ^{[2
]}

机构：

[1] CNR, Via Taurini 19, I-00185 Rome, Italy

[2] Politecn Torino, Dipartimento Elettron & Telecomunicaz, Turin, Italy

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2022年 / 144卷

关键词：

Central limit theorem; Hawkes processes; Poisson cluster processes; Poisson shot noise processes; Sharp deviations; Stable laws; PATH LARGE DEVIATIONS; RISK PROCESSES; RUIN PROBABILITY; TAIL;

D O I：

10.1016/j.spa.2021.11.008

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：

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.(c) 2021 Elsevier B.V. All rights reserved.

引用

页码：229 / 270

页数：42

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