Uniform Large deviations for infinite dimensional stochastic systems with jumps

TL;DR

This paper establishes uniform large deviation principles for infinite-dimensional stochastic systems driven by Brownian motions and Poisson jumps, using a variational representation approach.

Contribution

It extends large deviation principles to a broad class of infinite-dimensional systems with jumps, employing a novel variational formula.

Findings

Proves uniform large deviation principles for systems with jumps.

Develops a variational representation formula for infinite-dimensional stochastic processes.

Applies the framework to various types of infinite-dimensional Brownian motions.

Abstract

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational representation formula which for an infinite sequence of i.i.d real Brownian motions and a Poisson random measure was shown in [5].