Algorithms for Periodic Markov Chains

Abstract

The authors describe numerical algorithms to calculate the stationary probability vector of periodic Markov chains. Details including the proofs are published elsewhere. Firstly, the main properties of $P$- cyclic Markov chains are born in mind, and then the authors describe numerical methods for $P$-cyclic matrices. Later a reduced scheme is considered by transforming the original system of equations into a system of equations involving only a subset of the probability vector. Finally aggregation/disaggregation methods are described.