The Annals of Probability

A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes

Peter Clifford and Aidan Sudbury

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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.

Article information

Ann. Probab., Volume 13, Number 2 (1985), 558-565.

First available in Project Euclid: 19 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

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


Clifford, Peter; Sudbury, Aidan. A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes. Ann. Probab. 13 (1985), no. 2, 558--565. doi:10.1214/aop/1176993008.

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