Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes

TL;DR

This paper extends the Freidlin-Wentzell large deviation principle to pinned diffusion processes using rough path theory and quasi-sure analysis, broadening the understanding of stochastic process deviations.

Contribution

It introduces a novel approach combining rough path theory and quasi-sure analysis to establish large deviation principles for pinned diffusion processes.

Findings

Extended large deviation principles to pinned diffusions.

Applied rough path theory and quasi-sure analysis in new contexts.

Provided a framework for future research in stochastic deviations.

Abstract

Since T. Lyons invented rough path theory, one of its most successful applications is a new proof of Freidlin-Wentzell's large deviation principle for diffusion processes. In this paper we extend this method to the case of pinned diffusion processes under a mild ellipticity assumption. Besides rough path theory, our main tool is quasi-sure analysis, which is a kind of potential theory in Malliavin calculus.