Large Deviations for Rough Path Lifts of Watanabe's Pullbacks of Delta Functions

We study Donsker-Watanabe's delta functions associated with strongly hypoelliptic diffusion processes indexed by a small parameter. They are finite Borel measures on the Wiener space and admit a rough path lift. Our main result is a large deviation principle (LDP) of Schilder type for the lifted measures on the geometric rough path space as the scale parameter tends to zero. As a corollary, we obtain an LDP conjectured by Takanobu and Watanabe, which is a generalization of an LDP of Freidlin-Wentzell type for pinned diffusion processes.