An Exact Aggregation-Disaggregation Algorithm for Mandatory Set Decomposable Markov Chains

Abstract

Many Markov chain models have very large state spaces, making the computation of stationary probabilities very difficult. Often the structure and numerical properties of the Markov chain allows for more efficient computation through state aggregation and disaggregation. In this paper we develop an efficient exact single-pass aggregation-disaggregation algorithm that exploits structural properties of large finite irreducible mandatory set decomposable Markov chains. Mandatory set decomposable structure is a generalization of several other Markov chain structures for which exact aggregation-disaggregation algorithms exist.