# Precise deviations for Cox processes with a shot noise intensity

## TL;DR

This paper investigates the precise deviations of Cox processes with shot noise intensity, a model relevant in various fields, using the advanced mod-$\phi$ convergence method to derive new probabilistic results.

## Contribution

It introduces a novel application of the mod-$\phi$ convergence method to analyze deviations in shot noise Cox processes, enhancing understanding of their probabilistic behavior.

## Key findings

- Derived precise deviation results for shot noise Cox processes.
- Applied mod-$\phi$ convergence to a new class of stochastic processes.
- Provided tools for better risk assessment in fields like finance and insurance.

## 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.