47. Let {Xn, n 0} denote an ergodic Markov chain with limiting probabilities i . Define the...

47. Let {Xn, n 0} denote an ergodic Markov chain with limiting probabilities πi .

Define the process {Yn, n 1} by Yn = (Xn−1,Xn). That is, Yn keeps track of the last two states of the original chain. Is {Yn, n 1} a Markov chain? If so, determine its transition probabilities and find

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lim P(Yn = (i,j)}