Computable Error Bounds for Aggregated Markov Chains

摘要

This paper describes a method for computing the steady state probability vector of a nearly completely decomposable Markov chain. The method is closely related to one proposed by Simon and Ando and developed by Courtois. However, the method described here does not require the determination of a completely decomposable stochastic approximation to the transition matrix and hence it is applicable to matrices other than stochastic. An error analysis of the procedure is given which results in effectively computable error bounds. (Author)