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Dependence ordering for Markov processes on partially ordered spaces

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Hans Daduna  and
Ryszard Szekli
Hans Daduna*
Affiliation:
Hamburg University
Ryszard Szekli*
Affiliation:
Wrocław University
*
∗Postal address: Department of Mathematics, Hamburg University, Bundesstrasse 55, 20146 Hamburg, Germany.
∗∗Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: [email protected]
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Abstract

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We compare dependence in stochastically monotone Markov processes with partially ordered Polish state spaces using the concordance and supermodular orders. We show necessary and sufficient conditions for the concordance order to hold both in terms of the one-step transition probabilities for discrete-time processes and in terms of the corresponding infinitesimal generators for continuous-time processes. We give examples showing that a stochastic monotonicity assumption is not necessary for such orderings. We indicate relations between dependence orderings and, variously, the asymptotic variance-reduction effect in Monte Carlo Markov chains, Cheeger constants, and positive dependence for Markov processes.

Keywords

Concordance ordersupermodular orderstochastic monotonicitymonotone Markov processdependence orderCheeger constantassociationMCMC

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 793 - 814
Copyright
© Applied Probability Trust 2006 

Footnotes

Supported by the KBN, grant number 2P03A02023.

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