Large Deviations for Stochastic Differential Equations Driven by Semimartingales
Probability
2024-08-13 v3 Dynamical Systems
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.
Cite
@article{arxiv.1910.05720,
title = {Large Deviations for Stochastic Differential Equations Driven by Semimartingales},
author = {Qiao Huang and Wei Wei and Jinqiao Duan},
journal= {arXiv preprint arXiv:1910.05720},
year = {2024}
}