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Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Geometric Drift Conditions

Part of: Markov processes Special processes

Published online by Cambridge University Press:  04 January 2016

Hiroyuki Masuyama
Hiroyuki Masuyama*
Affiliation:
Kyoto University
*
∗ Postal address: Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan. Email address: masuyama@sys.i.kyoto-u.ac.jp
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Abstract

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In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally, we discuss the application of our results to GI/G/1-type Markov chains.

Keywords

Augmented truncationblock monotonicityblockwise dominancepathwise orderinggeometric drift conditionlevel-dependent QBDM/G/1-type Markov chainGI/M/1-type Markov chainGI/G/1-type Markov chain

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 1 , March 2015 , pp. 83 - 105
Copyright
© Applied Probability Trust 

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