Homogeneous decomposition of stochastic systems (Q1085980)

Recently, concerning the homogeneous whirl decomposition of stochastic systems, \textit{S. Kikuchi} and \textit{E. Fujino} [IECE Japan Trans. J 61-D, 827-833 (1978)] have suggested a decomposition theory (for any stochastic system) using the technique of 'state splitting'. However, their theory has the weak point that in the component stochastic system there exist several components whose transition matrices are pseudo-stochastic. In order to solve such a problem, this paper proposes a method to decompose any n-state (n\(\geq 3)\) stochastic system into m (m\(\geq 2)\) r-state \((2\leq r<n)\) q-neighbour (1\(\leq q\leq m-1)\) component stochastic systems whose transition matrices are nonpseudostochastic.