Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales

TL;DR

This paper develops a comprehensive framework for establishing large deviation principles for stochastic integrals and SDEs driven by broad classes of infinite-dimensional semimartingales, including Banach space-valued cases.

Contribution

It introduces a general approach with explicit rate functions for large deviations in infinite-dimensional stochastic systems, covering new classes of semimartingales.

Findings

Provides explicit rate functions for large deviations.

Applies results to various infinite-dimensional Markov processes.

Offers a systematic method for large deviation analysis in infinite dimensions.

Abstract

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of semimartingales considered is broad enough to cover Banach space-valued semimartingales and the martingale random measures. Simple usable expressions for the associated rate functions are given in this abstract setup. As illustrated through several concrete examples, the results presented here provide a new systematic approach to the study of large deviation principles for a sequence of Markov processes. Keywords: large deviations, stochastic integration, stochastic differential equations, exponential tightness, Markov processes, infinite dimensional semimartingales, Banach space-valued semimartingales