Precise deviations for Cox processes with a shot noise intensity

Zailei Cheng and Youngsoo Seol

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 23, 5850-5861

Abstract: We consider a Cox process with Poisson shot noise intensity which has been widely applied in insurance, finance, queue theory, statistic, and many other fields. Cox process is flexible because its intensity not only depends on the time but also can be considered as a stochastic process and so it can be considered as a two-step randomization procedure. Due to the structure of such models, a number of useful and general results can easily be established. In this paper, we study the fluctuations and precise deviations for shot noise Cox process using the recent mod-ϕ convergence method.

Date: 2019
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DOI: 10.1080/03610926.2018.1522351

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