Large deviations for multidimensional state-dependent shot noise processes

TL;DR

This paper establishes a large deviation principle for multidimensional state-dependent shot noise processes, extending previous results to more complex, higher-dimensional, and state-dependent models using the weak convergence approach.

Contribution

It introduces a large deviation principle for a broad class of multidimensional, state-dependent Poisson shot noise processes, generalizing earlier one-dimensional, state-independent results.

Findings

Proves a large deviation principle for multidimensional shot noise processes.

Extends known results to state-dependent and higher-dimensional models.

Uses weak convergence approach for the proof.

Abstract

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot noise processes. The result covers previously known large deviation results for one dimensional state-independent shot noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.