Open Access
2014 On the notion(s) of duality for Markov processes
Sabine Jansen, Noemi Kurt
Probab. Surveys 11: 59-120 (2014). DOI: 10.1214/12-PS206


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 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 many-body theory, reviewing known results and establishing some new connections.


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Sabine Jansen. Noemi Kurt. "On the notion(s) of duality for Markov processes." Probab. Surveys 11 59 - 120, 2014.


Published: 2014
First available in Project Euclid: 29 April 2014

zbMATH: 1292.60077
MathSciNet: MR3201861
Digital Object Identifier: 10.1214/12-PS206

Primary: 60J25
Secondary: 46N30 , 47D07 , 60J05

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.11 • 2014
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