  We consider a jump-diffusion process on a bounded domain with reflection at
the boundary, and establish long-term results for a general additive process of
its path. This includes the long-term behaviour of its occupation time and its
local time on the boundaries. We derive a characterization of the large
deviation rate function which quantifies the rate of exponential decay of
probabilities of rare events for paths of the process. The characterization
relies on a solution of a partial integro-differntial equation (PIDE) with
boundary constraints. We develop a practical implementation of our results in
terms of a numerical solution for the PIDE. We illustrate the method on a few
standard examples (Brownian motion, birth-death processes) and on a particular
jump-diffusion model arising from applications to biochemical reactions.
