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Math Help - Question about irreducibility ,recurrence of a Finite M. Chain

  1. #1
    Member mabruka's Avatar
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    Question about irreducibility ,recurrence of a Finite M. Chain

    hi!

    I just need to set the next implications straight since literature can be very confusing when talking about finite state space Markov chains.


    If X_n is an irreducible chain with finite state space then



    is X_n recurrent?



    even more, is X_n positive recurrent?


    I have found out the answer to both questions is positive but i would like to confirm it, is anybody sure about it? Can you think of any text where it explicitly shows the above results?


    Thank you!
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  2. #2
    Super Member Anonymous1's Avatar
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    Theorem. If C is a finite closed and irreducible set, then all states in C are recurrent.

    -Essentials of Stochastic Processes, Rick Durrett.
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  3. #3
    Member mabruka's Avatar
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    thank you, but what about positive recurrence?
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