Aggregation/Disaggregation Methods for P-cyclic Markov Chains

摘要

We present a new application of some aggregation/disaggregationiteration methods designed for finding stationary probability vectorsof p-stochastic matrices. Our main goal consists of provingconvergence of an aggregation/disaggregation iteration process basedon the Gauss-Seidel splitting of the matrix considered algorithm. Itshould be noted that besides p-cyclicity the matrix under consid-eration may be quite general, in particular, hypotheses concerningspectral properties of the matrix examined and its powers such asreality of its spectrum etc. and consistent ordering of the matrixitself are not required. finding stationary probability vectors of p-