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

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