Precise deviations for Cox processes with a shot noise intensity

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 depends on not only the time but also a stochastic process, 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 precise deviations for shot noise Cox process using the recent mod-$\phi$ convergence method.