An algorithm to compute the stochastically stable distribution of a perturbed markov matrix

Recently, some researchers have attempted to exploit state-aggregation techniques to compute stable distributions of high-dimensional Markov matrices (Gambin and Pokarowski, 2001). While these researchers have devised an efficient, recursive algorithm, their results are only approximate. We improve upon past results by presenting a novel state aggregation technique, which we use to give the first (to our knowledge) scalable, exact algorithm for computing the stochastically stable distribution of a perturbed Markov matrix. Since it is not combinatorial in nature, our algorithm is computationally feasible even for high-dimensional models.