  We study the large deviations of time-integrated observables of Markov
diffusions that have perfectly reflecting boundaries. We discuss how the
standard spectral approach to dynamical large deviations must be modified to
account for such boundaries by imposing zero-current conditions, leading to
Neumann or Robin boundary conditions, and how these conditions affect the
driven process, which describes how large deviations arise in the long-time
limit. The results are illustrated with the drifted Brownian motion and the
Ornstein-Uhlenbeck process reflected at the origin. Other types of boundaries
and applications are discussed.

Statistical Mechanics;Probability