ITERATIVE AGGREGATION DISAGGREGATION TECHNIQUES FOR NEARLY UNCOUPLED MARKOV-CHAINS

Iterative aggregation/disaggregation methods provide an efficient approach for computing the stationary probability vector of nearly uncoupled (also known as nearly completely decomposable) Markov chains. Three such methods that have appeared in the literature recently are considered and their similarities and differences are outlined. For each of these methods, a lemma is established, which shows that the unique fixed point of the iterative scheme is the left eigenvector corresponding to the dominant unit eigenvalue of the stochastic transition probability matrix. In addition, conditions are established for the convergence of two of these methods; convergence conditions for the third having already been established. All three methods are shown to have the same asymptotic rate of convergence.