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.
Publié le : 1985-05-14
Classification:
Markov chain,
absorbing barriers,
invasion processes,
infinite particle systems,
birth and death processes,
60J25,
60K35
@article{1176993008,
author = {Clifford, Peter and Sudbury, Aidan},
title = {A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 558-565},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993008}
}
Clifford, Peter; Sudbury, Aidan. A Sample Path Proof of the Duality for Stochastically Monotone Markov Processes. Ann. Probab., Tome 13 (1985) no. 4, pp. 558-565. http://gdmltest.u-ga.fr/item/1176993008/