@article{Jansen2012OnTN,
title={On the notion(s) of duality for Markov processes},
author={S. Jansen and N. 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… Expand