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.
Asymptotic analysis of Poisson shot noise processes, and applications / Torrisi, G. L.; Leonardi, E.. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - ELETTRONICO. - 144:(2022), pp. 229-270. [10.1016/j.spa.2021.11.008]
|Titolo:||Asymptotic analysis of Poisson shot noise processes, and applications|
|Data di pubblicazione:||2022|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.spa.2021.11.008|
|Appare nelle tipologie:||1.1 Articolo in rivista|