In chapter 4 of the book Introduction to probability models (10th edition), Ross states that in a Markov chain with a finite number of states, it is impossible to have a null recurrent state. He says "this can be shown". This isn't obvious to me at all. Null recurrent basically means the distribution of the number of steps till the chain comes back doesn't have a mean. Why are such distributions excluded? Not sure how to start proving this.
2026-04-09 16:58:52.1775753932
It is impossible to have a null recurrent state in a finite sized Markov chain?
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