Error Analysis in Nearly-Completely Decomposable Stochastic Systems

Abstract

The purpose of this paper is to analyze the accuracy of the Simon-Ando approximation for stochastic nearly-completely decomposable systems. Relations are established defining this accuracy as a function of the maximum degree of coupling (e) between aggregates, the conditioning and the indecomposability of these aggregates. A procedure is derived by which estimates in c2 may be computed from aggregate eigencharacteristics. Finally, the Simon-Ando approximation is shown to be optimal in block-stochastic matrices, and the accuracy achievable by higher-order aggregation is examined.