A sample path proof of the duality for stochastically monotone Markov processes
This paper provides an explanation of \textit{D. Siegmund}'s duality [ibid. 4, 914-924 (1976; Zbl 0364.60109)] 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.
scientific article; zbMATH DE number 3897958