publication . Article . Preprint . 2015

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

Hiroyuki Masuyama;
Open Access
  • Published: 05 Jun 2015 Journal: SIAM Journal on Matrix Analysis and Applications, volume 37, pages 877-910 (issn: 0895-4798, eissn: 1095-7162, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
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 Mark...
Persistent Identifiers
Subjects
free text keywords: Mathematics - Probability, 60J10, 60J22, 60K25, Markov chain mixing time, Continuous-time Markov chain, Truncation, Applied mathematics, Additive Markov chain, Matrix analytic method, Balance equation, Combinatorics, Monotone polygon, Mathematics, Markov chain

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