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Bounded truncation error for long-run averages in infinite Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  30 March 2016

Hendrik Baumann  and
Werner Sandmann
Hendrik Baumann*
Affiliation:
Clausthal University of Technology
Werner Sandmann*
Affiliation:
University of Derby
*
∗ Postal address: Department of Applied Stochastics and Operations Research, Clausthal University of Technology, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany. Email address: hendrik.baumann@tu-clausthal.de
∗∗ Postal address: School of Computing and Mathematics, University of Derby, Kedleston Road, Derby DE22 1GB, UK.
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Abstract

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We consider long-run averages of additive functionals on infinite discrete-state Markov chains, either continuous or discrete in time. Special cases include long-run average costs or rewards, stationary moments of the components of ergodic multi-dimensional Markov chains, queueing network performance measures, and many others. By exploiting Foster-Lyapunov-type criteria involving drift conditions for the finiteness of long-run averages we determine suitable finite subsets of the state space such that the truncation error is bounded. Illustrative examples demonstrate the application of this method.

Keywords

Infinite Markov chainadditive functionallong-run averagestate space truncationbounded truncation errorFoster-Lyapunov-type criteriondrift condition

MSC classification

Primary: 60J22: Computational methods in Markov chains
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 609 - 621
Copyright
Copyright © 2015 by the Applied Probability Trust 

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