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May, 1985 A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes
Peter Clifford, Aidan Sudbury
Ann. Probab. 13(2): 558-565 (May, 1985). DOI: 10.1214/aop/1176993008


This paper provides an explanation of Siegmund's duality for absorbing and reflecting Markov processes by means of a graphical representation of the type used in the analysis of infinite particle systems. It is shown that coupled realisations of a Markov process conditioned to start at each of the points of the state space can be generated on the same probability space in such a way that their ordering is preserved. Using the same probability space a specific construction is then given for the dual process.


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Peter Clifford. Aidan Sudbury. "A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes." Ann. Probab. 13 (2) 558 - 565, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0563.60062
MathSciNet: MR781422
Digital Object Identifier: 10.1214/aop/1176993008

Primary: 60J25
Secondary: 60K35

Keywords: absorbing barriers , birth and death processes , infinite particle systems , invasion processes , Markov chain

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 2 • May, 1985
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