We consider long-run averages of additive functionals on infinite discrete-state Markov chains, either continuous or discrete in time. Special cases include long-run average costs or rewards, stationary moments of the components of ergodic multi-dimensional Markov chains, queueing network performance measures, and many others. By exploiting Foster-Lyapunov-type criteria involving drift conditions for the finiteness of long-run averages we determine suitable finite subsets of the state space such that the truncation error is bounded. Illustrative examples demonstrate the application of this method.
"Bounded truncation error for long-run averages in infinite Markov chains." J. Appl. Probab. 52 (3) 609 - 621, September 2015. https://doi.org/10.1239/jap/1445543835