ABSTRACT
All Markov chains treated in this book have a fi nite number of states. Recall from Section 1.9 that a reducible Markov chain has both recurrent states and transient states. The state space for a reducible chain can be partitioned into one or more mutually exclusive closed communicating classes of recurrent states plus a set of transient states. A closed communicating class of recurrent states is often called a recurrent class or a recurrent chain. The state space for a reducible unichain can be partitioned into one recurrent chain plus a set of transient states. The state space for a reducible multichain can be partitioned into two or more mutually exclusive recurrent chains plus a set of transient states. There is no interaction among different recurrent chains within a reducible multichain. Hence, each recurrent chain can be analyzed separately by treating it as an irreducible Markov chain. A reducible chain, which starts in a transient state, will eventually leave the set of transient states to enter a recurrent chain, within which it will continue to make transitions indefi nitely.
