The noisy voter-exclusion process

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 process to obtain information concerning the original process. This paper introduces 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 the coupling method.