On the notion(s) of duality for Markov processes
Abstract
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 semigroups. The analytic framework builds on the notion of dual pairs, convex geometry, and Hilbert spaces. In addition, we formalize the notion of pathwise duality as it appears in population genetics and interacting particle systems. We discuss the relation of duality with rescalings, stochastic monotonicity, intertwining, symmetries, and quantum manybody theory, reviewing known results and establishing some new connections.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1210.7193
 Bibcode:
 2012arXiv1210.7193J
 Keywords:

 Mathematics  Probability;
 Mathematics  Functional Analysis;
 60J25 (Primary) 46N30;
 47D07;
 60J05 (Secondary)
 EPrint:
 52 pages, 3 tables, 3 figures, revised version