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Stochastic domination and Markovian couplings

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

F. Javier López ,
Servet Martínez  and
Gerardo Sanz
F. Javier López*
Affiliation:
Universidad de Zaragoza
Servet Martínez*
Affiliation:
Universidad de Chile
Gerardo Sanz*
Affiliation:
Universidad de Zaragoza
*
∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain.
∗∗ Postal address: Departamento de Ingeniería Matemática y Centro de Modelamiento Matemático UMR 2071, CNRS, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile. Email address: gerardo.sanz@posta.unizar.es
∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain.
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Abstract

For continuous-time Markov chains with semigroups P, P' taking values in a partially ordered set, such that P ≤ stP', we show the existence of an order-preserving Markovian coupling and give a way to construct it. From our proof, we also obtain the conditions of Brandt and Last for stochastic domination in terms of the associated intensity matrices. Our result is applied to get necessary and sufficient conditions for the existence of Markovian couplings between two Jackson networks.

Keywords

Markov chainorder-preserving couplingHahn-Banach theoremJackson network

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 4 , December 2000 , pp. 1064 - 1076
Copyright
Copyright © Applied Probability Trust 2000 

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