I am curious about a proof for the generalization of the basic limit theorem in stochastic processes. That is:
$\lim \limits_{n \to \infty} P_{jj}^{(ns)} =\frac{s}{t_{jj}}$ where s is the period of the irreducible and positive recurrent markov chain and $t_{jj}$ is the mean recurrence time. I feel like this proof should be available in common textbooks but I just cannot seem to find..If someone could point me towards a reference or give me some hints on how I can approach the proof..I would appreciate it!
Thanks