Let {X n , n ≥ 1} denote a irreducible recurrent Markov chain having a countable state space. Now consider a new stochastic process {Y n , n 0} that only accepts values of the Markov chain that are...

Let {X_n, n ≥ 1} denote a irreducible recurrent Markov chain having a countable state space. Now consider a new stochastic process {Y_n, n 0} that only accepts values of the Markov chain that are between 0 and some integer m. For instance, if m = 3 and X₁
= 1, X₂
= 3, X₃
= 5, X₄
= 6, X₅
= 2, then Y₁
= 1, Y₂
= 3, Y₃
= 2.