# Thread: Null-recurrent Markov Chain

1. ## 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.

2. Originally Posted by raheel88
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...

3. Originally Posted by Laurent
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.