  The symmetric exclusion process and the voter model are two interacting
particle systems for which a dual finite particle system allows one to
characterize its invariant measures. Adding spontaneous births and deaths to
the two processes still allows one to use the dual to obtain information about
the original process. We study the noisy voter-exclusion process which
generalizes these processes by allowing for all of these interactions to take
place. The dual process is used to characterize its invariant measures under
various circumstances. Finally, an ergodic theorem for a related process is
proved using couplings.
