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 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. MSC2010: primary 60G55; secondary 60F05, 60F10.