Increasing couplings for interacting particle systems

Classical stochastic comparison results for spin systems are generalized to more complex interacting particle systems. The state space of each site is a finite partially ordered set and several sites may simultaneously change status. Two ways of obtaining comparison conditions are considered. The first one consists in adapting to interacting particle systems a result by Massey for Markov processes on countable spaces. The second is based on the explicit construction of Markov couplings. In particular, a generalization of the Vasershtein coupling for spin systems is used.