Consider a process {Xn, n = 0,1, ... }, which takes on the values 0,1, or...

Question:

Consider a process {Xn, n = 0,1, ... }, which takes on the values 0,1, or 2. Suppose P{Xn+1 = ||Xn = i, Xn-1 = in-1,..., X0 = i +0} = when n is even when n is odd where - P = - Phl = 1, i = 0,1,2. Is {Xn, n = 0,1,... } a time-homogeneous Markov chain? If not, then show how, by enlarging the state space, we may transform it into a time- homogeneous Markov chain.

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