Aggregation/Disaggregation Methods for Computing the Stationary Distribution of a Markov Chain

Abstract

We implement and analyse aggregation/disaggregation procedures constructed to accelerate the convergence of successive approximation methods suitable for computing the stationary distribution of a finite Markov chain. We define six of these methods and analyse them in detail. In particular, we show that some existing procedures lie in the aggregation/disaggregation framework we set, and hence can be considered as special cases. Also, for all described methods, we identify cases where they are promising. Numerical examples for the applications of some of the methods for nearly completely decomposable stochastic matrices are given as well.