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 $\displaystyle X_n$ is an irreducible chain with finite state space then

is $\displaystyle X_n$ recurrent?

even more, is $\displaystyle X_n$ 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!