On regularly perturbed fundamental matrices ✩

In this note we characterize regular perturbations of finite state Markov chains in terms of continuity properties of its fundamental matrix. A perturbation turns out to be regular if and only if the fundamental matrix can be approximated by the discounted deviation from stationarity for small perturbation parameters. We also give bounds to asses the quality of the approximation. © 2007 Elsevier Inc. All rights reserved.