A Whirl decomposition of stochastic systems based on the substitution property
Taiho Kanaoka, Shingo Tomita · IEEE Transactions on Systems Man and Cybernetics · 1983
A new method is proposed for realizing a stochastic system from interconnected smaller stochastic systems. Each smaller stochastic system considered is composed of two states. The basic tool is the partition with a substitution property which exists on the transition matrix of the interconnected stochastic system. Using the authors' method, a stochastic system withnstates is decomposed intom(m≥n-1) component systems where each system has two states. The following results are derived: for a given outer input, each component system hasn-1 state transition matrices; a relationship exists among some entries of transition matrices; and the whole system is composed ofmcomponent stochastic systems, butm-n+1 component systems are selected freely.