prove ergodic theorem for finite irreducible, aperiodic Markov Chain

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State and prove ergodic theorem for finite irreducible, aperiodic Markov Chain with transition probability matrix $P=(p_ij)$.




I know what irreducible, aperiodic means. But I do not understand about what theorem it is referring. More precisely, what are the things I need to prove.



I know that if a finite markov chain is irreducible, it is called ergodic markov chain. But what to prove here if that is a definition. So what to prove here?



Thanks for any help.







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    up vote
    1
    down vote

    favorite













    State and prove ergodic theorem for finite irreducible, aperiodic Markov Chain with transition probability matrix $P=(p_ij)$.




    I know what irreducible, aperiodic means. But I do not understand about what theorem it is referring. More precisely, what are the things I need to prove.



    I know that if a finite markov chain is irreducible, it is called ergodic markov chain. But what to prove here if that is a definition. So what to prove here?



    Thanks for any help.







    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite












      State and prove ergodic theorem for finite irreducible, aperiodic Markov Chain with transition probability matrix $P=(p_ij)$.




      I know what irreducible, aperiodic means. But I do not understand about what theorem it is referring. More precisely, what are the things I need to prove.



      I know that if a finite markov chain is irreducible, it is called ergodic markov chain. But what to prove here if that is a definition. So what to prove here?



      Thanks for any help.







      share|cite|improve this question













      State and prove ergodic theorem for finite irreducible, aperiodic Markov Chain with transition probability matrix $P=(p_ij)$.




      I know what irreducible, aperiodic means. But I do not understand about what theorem it is referring. More precisely, what are the things I need to prove.



      I know that if a finite markov chain is irreducible, it is called ergodic markov chain. But what to prove here if that is a definition. So what to prove here?



      Thanks for any help.









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 23 at 10:27









      Stat_prob_001

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