  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.
