Applications of Pazʹs inequality to perturbation bounds for Markov chains

In several papers Meyer, singly and with coauthors, established the usefulness of the group generalized inverse in the study and computations of various aspects of Markov chains. Here we are interested in those results which concern bounds on the condition number of the chain and on the error in the computation of the stationary distribution vector. We show that a lemma due to Paz can be used to improve, sometimes by a factor of 2, some of the constants in the bounds obtained in the aforementioned papers.