  The large deviations principle for the empirical measure for both continuous
and discrete time Markov processes is well known. Various expressions are
available for the rate function, but these expressions are usually as the
solution to a variational problem, and in this sense not explicit. An
interesting class of continuous time, reversible processes was identified in
the original work of Donsker and Varadhan for which an explicit expression is
possible. While this class includes many (reversible) processes of interest, it
excludes the case of continuous time pure jump processes, such as a reversible
finite state Markov chain. In this paper, we study the large deviations
principle for the empirical measure of pure jump Markov processes and provide
an explicit formula of the rate function under reversibility.
