The Annals of Probability
- Ann. Probab.
- Volume 13, Number 2 (1985), 558-565.
A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes
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.
Ann. Probab., Volume 13, Number 2 (1985), 558-565.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.aop/1176993008