Advances in Applied Probability

Error bounds for augmented truncations of discrete-time block-monotone Markov chains under geometric drift conditions

Hiroyuki Masuyama

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 1 (2015), 83-105.

Dates
First available in Project Euclid: 31 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1427814582

Digital Object Identifier
doi:10.1239/aap/1427814582

Mathematical Reviews number (MathSciNet)
MR3327316

Zentralblatt MATH identifier
1310.60106

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Augmented truncation block monotonicity blockwise dominance pathwise ordering geometric drift condition level-dependent QBD M/G/1-type Markov chain GI/M/1-type Markov chain GI/G/1-type Markov chain

Citation

Masuyama, Hiroyuki. Error bounds for augmented truncations of discrete-time block-monotone Markov chains under geometric drift conditions. Adv. in Appl. Probab. 47 (2015), no. 1, 83--105. doi:10.1239/aap/1427814582. https://projecteuclid.org/euclid.aap/1427814582


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