Attractive n-type contact processes

Abstract

Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is called attractive. A benefit of attractiveness is that it simplifies certain calculations, one of which is the ability to use some computational algorithms to sample exactly from the stationary distribution of an ergodic process. Monotonicity is well understood for spin systems such as the contact process. Spin systems only include two particle types however, while in many applied models, it is desirable to include more species of particles. In this paper a general framework of monotonicity will be outlined for a certain class of multitype contact processes.