On the notion(s) of duality for Markov processes

Jansen, Sabine and Kurt, Noemi (2014) On the notion(s) of duality for Markov processes. Probability Surveys, 11. pp. 59-120. ISSN 1549-5787

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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 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 16 Jan 2017 14:40
Last Modified: 08 Mar 2017 06:20
URI: http://sro.sussex.ac.uk/id/eprint/66205

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