Let {Xn,n 0} denote an ergodicMarkov chain with limiting probabilities i . Define the process {Yn,n 1}

Let {Xn,n 0} denote an ergodicMarkov 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{Y, (i, j)}