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Math Help - Markov chaines periodic aperiodic

  1. #1
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    Markov chaines periodic aperiodic

    How do we know whether they are periodic or aperiodic and how do we work out what is the periodicty.

    Thanks.
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    Hello,

    Have you read that : Markov chain - Wikipedia, the free encyclopedia ???
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  3. #3
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    Im still confused

    I have a matrix \begin{array}{cccc}0.1&0.1&0&0.8\\0&0.9&0.1&0\\0&1  &0&0\\0.4&0&0&0.6\end{array}

    The classes are

    {0} open
    {1,2} closed
    {3} open

    How do i do periodicity, thanks for your help in advance.
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  4. #4
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    a state is periodic if the probability of
    returning to the state is zero except at regular intervals
    eg if you go from 0 to 2 in a markov chain it should be the same number of steps to go from 2 to 0
    Last edited by asingh88; January 13th 2010 at 05:09 PM.
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  5. #5
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    Quote Originally Posted by adam_leeds View Post
    Im still confused

    I have a matrix \begin{array}{cccc}0.1&0.1&0&0.8\\0&0.9&0.1&0\\0&1  &0&0\\0.4&0&0&0.6\end{array}

    The classes are

    {0} open
    {1,2} closed
    {3} open

    How do i do periodicity, thanks for your help in advance.
    Hmmm draw a sketch with the arrows.
    What do you call open and closed ? I know transient, absorbing and recurrent... (Markov chain - Wikipedia, the free encyclopedia)
    And all are transient except 2, which is absorbing, because once you're in 2, you can't leave it since it returns to itself with probability 1.

    Following from the criterion for the period of a chain, I'd advise you to consider i=2. And you should conclude with ease, it's not very hard
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