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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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

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

First available in Project Euclid: 31 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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