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

Hiroyuki Masuyama

doi:10.1137/15m1024743

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arXiv · 1506.01789

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

Hiroyuki Masuyama

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Abstract

This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to present an upper bound for the total variation distance between the stationary probability vectors of a block-monotone Markov chain and its LC-block-augmented truncation. The main result is extended to Markov chains that themselves may not be block monotone but are block-wise dominated by block-monotone Markov chains satisfying modified drift conditions. Finally, as an application of the obtained results, the GI/G/1-type Markov chain is considered.

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BibTeX RIS

Hiroyuki Masuyama. 2015-06-05. Error bounds for augmented truncations of discrete-time block-monotone Markov chains under subgeometric drift conditions. https://doi.org/10.1137/15m1024743

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