A sample path proof of the duality for stochastically monotone Markov processes
type: Item
instance of: scholarly article
title: A sample path proof of the duality for stochastically monotone Markov processes
zbMATH Open document ID: 0563.60062
author: Peter Clifford
author: Aidan Sudbury
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 3897958
zbMATH Keywords: birth and death processes
zbMATH Keywords: infinite particle systems
zbMATH Keywords: dual process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993008
OpenAlex ID: W1987279787
DOI: 10.1214/AOP/1176993008
description: scientific article; zbMATH DE number 3897958