Abstrakt
In the study of interacting particle systems duality is an important tool used to prove various types of long-time behavior, for example convergence to an invariant distribution. The two most used types of dualities are additive and cancellative dualities, which we are able to treat in a unied framework considering commutative monoids (i.e. semigroups containing a neutral element) as cornerstones of such a duality.
For interacting particle systems on local state spaces with more than two elements this approach revealed formerly unknown dualities. As an application of one of the newly found dualities a convergence result of a combination of the contact process and its cancellative version, formerly known as the annihilating branching process, is presented.