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