On the notion(s) of duality for Markov processes

@article{Jansen2012OnTN,
  title={On the notion(s) of duality for Markov processes},
  author={Sabine Jansen and Noemi Kurt},
  journal={Probability Surveys},
  year={2012},
  volume={11},
  pages={59-120}
}
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory and give functional analytic results including existence and uniqueness criteria and a comparison of the spectra of dual semi-groups. The analytic framework builds on the notion of dual pairs, convex geometry, and Hilbert spaces. In addition, we formalize the… 

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