On censored Markov chains, best augmentations and aggregation disaggregation procedures

Consider the stationary distribution of a Markov chain censored to a subset of the original state space. ft can be approximated by augmenting the subs tochastic matrix T representing transition probabilities in this subset int o a stochastic matrix and solving for the corresponding stationary distribu tion. For the case of nearly uncoupled chains, under some mild technical as sumptions, we find the best augmentation in the sense of minimizing the res ulting error-bound, out of all augmentations which are based solely on the data given by T. Doing that for all submatrices representing transition pro babilities inside all the subsets of a nearly uncoupled Markov ch ain const itutes part of the aggregation step in a standard aggregation/disaggregatio n procedure for approximating the stationary distribution of the original. process.