# Pathwise Duals of Monotone and Additive Markov Processes

@article{Sturm2015PathwiseDO, title={Pathwise Duals of Monotone and Additive Markov Processes}, author={Anja Sturm and Jan M. Swart}, journal={Journal of Theoretical Probability}, year={2015}, volume={31}, pages={932-983} }

This paper develops a systematic treatment of monotonicity-based pathwise dualities for Markov processes taking values in partially ordered sets. We show that every Markov process that takes values in a finite partially ordered set and whose generator can be represented in monotone maps has a pathwise dual process. In the special setting of attractive spin systems, this has been discovered earlier by Gray. We show that the dual simplifies a lot when the state space is a lattice (in the order…

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