Error bounds for augmented truncations of discrete-time block-monotone Markov chains under subgeometric drift conditions
Probability
2016-11-23 v5
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.
Keywords
Cite
@article{arxiv.1506.01789,
title = {Error bounds for augmented truncations of discrete-time block-monotone Markov chains under subgeometric drift conditions},
author = {Hiroyuki Masuyama},
journal= {arXiv preprint arXiv:1506.01789},
year = {2016}
}