Large Deviations for Stochastic Differential Equations Driven by Semimartingales

TL;DR

This paper establishes a large deviation principle for solutions of stochastic differential equations driven by semimartingales, linking the deviations of the noise-control pairs to those of the solutions without requiring joint tightness assumptions.

Contribution

It introduces conditions based on semimartingale characteristics that ensure large deviations for SDE solutions driven by semimartingales, without joint exponential tightness assumptions.

Findings

Large deviation principle proven for SDEs driven by semimartingales.

Conditions relate characteristics of semimartingales to solution deviations.

No need for joint exponential tightness assumptions.

Abstract

We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs satisfy a large deviation principle with some good rate function, so do the solution processes. There is no joint exponential tightness assumption for noise-control-solution triplets and no uniform exponential tightness assumption for noise.