Let (X, n 0] denote an ergodic Markov chain with limiting probabilities. Define the process (Y, n

Question:

Let (X, n 0] denote an ergodic Markov chain with limiting probabilities. Define the process (Y, n 1] by Y = (x-1, X). That is, Y, keeps track of the last two states of the original chain. Is [Y, n 1) a Markov chain? If so, determine its transition probabilities and find lim P{Y, = (I,J))

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