Cyclic decomposition of finite stochastic systems

摘要

Existence conditions and techniques for partitioning the states of finite stochastic systems into cyclic classes are given in this paper. For the special class of preserved finite stochastic systems, such cyclic partitions are shown to be evaluated, explicity, in terms of those cyclic partitions associated with the finite Markov chains embedded in the system. Generalizations and applications of above results to the periodic decomposition of stochastic sequential machines are investigated.