Abstrakt
A theory of dual processes for attractive spin systems was developed by Gray. Based on Gray's work, monotonicity-based pathwise dualities for Markov processes in general and interacting particle systems in particular were systematically investigated by Sturm and Swart.
However, the authors only prove the well-definedness of the dual process if started from finite initial states. We show how to construct a well-defined pathwise dual process of a monotone interacting particle system that can also be started from an infinite initial state.
This then allows us to study invariant laws of the dual process and connect them to properties of the original interacting particle system.