Suppose a recurrent Markov chain has period d and let S m , 1 ≤ m ≤ d, be the mth subset in the sense of Theorem XXXXXXXXXXAssume the states are numbered so that the first s 1 states are the states of...




Suppose a recurrent Markov chain has period d and let Sm, 1 ≤ m ≤ d, be the mth subset in the sense of Theorem 4.2.3. Assume the states are numbered so that the first s1
states are the states of S1, the next s2
are those of S2, and so forth. Thus the matrix [P] for the chain has the block form given by

Theorem 4.2.3. If a recurrent class C in a finite-state Markov chain has period d, then the states in C can be partitioned into d subsets, S1, S2, . . . , Sd, in such a way that all transitions from S1
go to S2, all from S2
go to S3, and so forth up to Sd1
to Sd. Finally, all transitions from Sd
go to S1.




May 08, 2022
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