University of Sussex
Browse

File(s) under permanent embargo

On the notion(s) of duality for Markov processes

journal contribution
posted on 2023-06-09, 04:44 authored by Sabine Jansen, Noemi Kurt
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Probability Surveys

ISSN

1549-5787

Publisher

Institute of Mathematical Statistics

Volume

11

Page range

59-120

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-16

First Compliant Deposit (FCD) Date

2017-01-13

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC