An Algorithm to Compute the Stochastically Stable Distribution of a Perturbed Markov Matrix

of “An Algorithm to Compute the Stochastically Stable Distribution of a Perturbed Markov Matrix” by John R. Wicks, Ph.D., Brown University, August 2008. 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 highdimensional models. An Algorithm to Compute the Stochastically Stable Distribution of a Perturbed Markov Matrix by John R. Wicks B. S., Mathematics/Computer Science and Economics, Carnegie Mellon University, 1983 M. S., Mathematics, Carnegie Mellon University, 1983 S. M., Mathematics, University of Chicago, 1983 Ph. D., Mathematics, University of Chicago, 1990 Sc. M., Computer Science, Brown University, 2007 Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in the Department of Computer Science at Brown University Providence, Rhode Island August 2008 c © Copyright 2008 by John R. Wicks