Model reduction of irreducible Markov chains

We are interested in developing computational tools for reducing the state space of irreducible Markov chains. As means of decreasing the dimensionality of a given Markov chain we study the concept of aggregation. The approximation error between the original and the reduced order model is captured by a metric that penalizes the asymptotic deviation of the outputs of the two systems. For the case of nearly completely decomposable Markov chains we demonstrate how a decomposition approach can be used to derive a low order model of good fidelity.