Continuation. Consider the processes Xn and Yn in the preceding exercise with the history Hn changed to Hn ≡ {X k−1, Y k+1 , k ≤ n−1, Xn−1 } (it no longer contains Yn). Is Xn is a Markov chain? If so...

Continuation. Consider the processes
_Xn
and Yn in the preceding exercise with the history Hn changed to Hn ≡ {X_k−1,
Y_k+1, k ≤ n−1,
_Xn−1} (it no longer contains Yn). Is
_Xn
is a Markov chain? If so specify its transition probabilities. Answer this under the additional assumption that Gi,i (A) = P{Yn+1 ∈ A|_Xn
= i, Y_n
= i  } is independent of n