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

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.

References in corpus (6)

• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• Approximating Markov chains and V-geometric ergodicity via weak perturbation theory
• Error bounds for last-column-block-augmented truncations of block-structured Markov chains
• Continuous-time block-monotone Markov chains and their block-augmented truncations
• Ergodicity for the $GI/G/1$-type Markov Chain
• A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications

Cited by in corpus (2)

• Error bounds for last-column-block-augmented truncations of block-structured Markov chains
• Continuous-time block-monotone Markov chains and their block-augmented truncations