Consider an homogeneous, ergodic Markov Chain with a finite state space , the transition matrix and the stationnary distribution .
Given that is also the initial distribution, what is the limit:
One approach is to use Renewal Theory and consider probabilities that for the first time. However, my application of this approach gives the same result as if each step of the chain was completely independent from the previous one, hence any past one. Could this be right?
Thanks for your help.