Large deviations for the empirical measure of a diffusion via weak convergence methods

We consider the large deviation principle for the empirical measure of a diffusion in Euclidean space, which was first established by Donsker and Varadhan. We employ a weak convergence approach and obtain a characterization for the rate function that is dual to the one obtained by Donsker and Varadhan, and which allows us to evaluate the variational form of the rate function for both reversible and nonreversible diffusions.