Asymptotic analysis of Poisson shot noise processes, and applications

Giovanni Luca Torrisi and Emilio Leonardi

Stochastic Processes and their Applications, 2022, vol. 144, issue C, 229-270

Abstract: 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.

Keywords: Central limit theorem; Hawkes processes; Poisson cluster processes; Poisson shot noise processes; Sharp deviations; Stable laws (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.11.008

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