  Our aim is to unify and extend the large deviation upper and lower bounds for
the occupation times of a Markov process with $L_2$ semigroups under minimal
conditions on the state space and the process trajectories; for example, no
strong Markov property is needed. The methods used here apply in both
continuous and discrete time. We present the proofs for continuous time only
because of the inherent technical difficulties in that situation; the proofs
can be adapted for discrete time in a straightforward manner.
