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On the notion(s) of duality for Markov processes
journal contribution
posted on 2023-06-09, 04:44 authored by Sabine Jansen, Noemi KurtWe 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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Publication status
- Published
File Version
- Published version
Journal
Probability SurveysISSN
1549-5787Publisher
Institute of Mathematical StatisticsExternal DOI
Volume
11Page range
59-120Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-16First Compliant Deposit (FCD) Date
2017-01-13Usage metrics
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