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

Abstract

This paper studies 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 may not be block-monotone but is block-wise dominated by a block-monotone Markov chain. Finally we discuss the application of our results to GI/G/1-type Markov chains.