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I don't understand why the only state with period > 1 is 1 Let's take state 2 for example, what's the period for state 2? Another question is, does an absorbing state(state 4 in this example) only have period of 1?

  • 1
    $\begingroup$ Good question. See stats.stackexchange.com/questions/48838. Perhaps you should consult the source of your image to find out precisely what its definition of "period" is. Perhaps it's non-standard. $\endgroup$
    – whuber
    Jul 5, 2016 at 14:00

1 Answer 1


An absorbing state has a preriod of 1, yes. Because there is a loop on himself. It's true only if it's not in an absorbing class.

But states 1,2,3,5 and 6 are in the same class of communication (you can go to an other state of the class and come back if you want) so they have the same period. which is 3.

If you gave us the source maybe there is some explanation.

Is this Markov chain irreducible?

You can read that, it can be helpful.

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    $\begingroup$ (+1) It might help to explain why state 1, which can be returned to only in 3 steps, has the same period as e.g. 2, which can be returned to in either 3 or 6 steps. $\endgroup$ Jul 7, 2016 at 10:16

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