Large Deviations for Small Noise Hypoelliptic Diffusion Bridges on Sub-Riemannian Manifolds

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.