Large deviations for stochastic differential delay equations with L\'evy noises

TL;DR

This paper establishes a large deviation principle for stochastic differential delay equations influenced by Brownian motions and Poisson measures, using the weak convergence method to analyze rare event probabilities.

Contribution

It introduces a large deviation framework for delay equations with Lévy noise, extending existing theories to more complex stochastic systems.

Findings

Large deviation principle successfully established for the system.

Methodology applicable to a broad class of stochastic delay equations.

Provides theoretical foundation for analyzing rare events in systems with Lévy noise.

Abstract

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.