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Math Help - Null-recurrent Markov Chain

  1. #1
    Junior Member raheel88's Avatar
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    Null-recurrent Markov Chain

    Hi all,

    I have the following problem.
    I want to define a Markov chain whereby all states are null recurrent. The condition is that the chain needs to be finite and irreducible.

    My main issue is understanding null-recurrence. I understand it to be a chain where the expected time of first return to a state i is infinite.
    But wouldn't that make that state transient?

    Very confused about this, so any help on the matter would be greatly appreciated.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by raheel88 View Post
    I want to define a Markov chain whereby all states are null recurrent. The condition is that the chain needs to be finite and irreducible.
    If a chain is finite and irreducible, its states are positive recurrent. Null recurrence only occurs for infinite chains...
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  3. #3
    Junior Member raheel88's Avatar
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    Quote Originally Posted by Laurent View Post
    If a chain is finite and irreducible, its states are positive recurrent. Null recurrence only occurs for infinite chains...
    Thank you laurent...i knew there was something i was missing.
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