Large deviations for small noise hypoelliptic diffusion bridges on sub-Riemannian manifolds

TL;DR

This paper establishes a large deviation principle for hypoelliptic diffusion bridges on sub-Riemannian manifolds using advanced probabilistic and geometric techniques.

Contribution

It introduces a large deviation framework for hypoelliptic diffusions on sub-Riemannian manifolds, combining rough path theory and Malliavin calculus.

Findings

Proves a Freidlin-Wentzell type large deviation principle for hypoelliptic diffusions.

Develops methods to handle the geometric complexity of sub-Riemannian manifolds.

Extends large deviation theory to a new class of stochastic processes on manifolds.

Abstract

In this paper we study a large deviation principle of Freidlin-Wentzell type for pinned hypoelliptic diffusion measures associated with a natural sub-Laplacian on a compact sub-Riemannian manifold. To prove this large deviation principle, we use rough path theory and manifold-valued Malliavin calculus.