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.