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

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 lim n→∞ P{Yn = (i,j)}