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September 2015 Bounded truncation error for long-run averages in infinite Markov chains
Hendrik Baumann, Werner Sandmann
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J. Appl. Probab. 52(3): 609-621 (September 2015). DOI: 10.1239/jap/1445543835

Abstract

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.

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Hendrik Baumann. Werner Sandmann. "Bounded truncation error for long-run averages in infinite Markov chains." J. Appl. Probab. 52 (3) 609 - 621, September 2015. https://doi.org/10.1239/jap/1445543835

Information

Published: September 2015
First available in Project Euclid: 22 October 2015

zbMATH: 1326.60107
MathSciNet: MR3414980
Digital Object Identifier: 10.1239/jap/1445543835

Subjects:
Primary: 60J22
Secondary: 60J10 , 60J27 , 60J28

Keywords: additive functional , bounded truncation error , drift condition , Foster-Lyapunov-type criterion , Infinite Markov chain , long-run average , state space truncation

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 3 • September 2015
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