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}
}
  • A. Sturm, J. Swart
  • Published 21 October 2015
  • Mathematics
  • Journal of Theoretical Probability
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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