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On a Comparison Result for Markov Processes

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

Ludger Rüschendorf
Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
∗Postal address: Department of Mathematical Stochastics, University of Freiburg, Eckerstrasse 1, D-79104 Freiburg, Germany. Email address: ruschen@stochastik.uni-freiburg.de
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Abstract

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A comparison theorem is stated for Markov processes in Polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In particular, Liggett's theorem on the association of Markov processes is a consequence of this comparison result.

Keywords

Association of Markov processesstochastic monotonicityinfinitesimal generatorstochastic ordering

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 279 - 286
Copyright
Copyright © Applied Probability Trust 2008 

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