Error bounds for augmented truncation approximations of continuous-time Markov chains

This paper considers the augmented truncation approximation of the generator of an ergodic continuous-time Markov chain with a countably infinite state space. The main purpose of this paper is to present bounds for the absolute difference between the stationary distributions of the original generator and its augmented truncation. As examples, we apply the bounds to an $M∕M∕s$ retrial queue and an upper Hessenberg Markov chain.