Consider a process {Xn, n = 0, 1,...}, which takes on the values 0, 1, or 2.

Suppose P{Xn+1 = j|Xn = i, Xn−1 = in−1,..., X0 = i0}

=

PI i j, when n is even PII i j , when n is odd where 2 j=0 PI i j = 2 j=0PII i j = 1,i = 0, 1, 2. Is {Xn, n 0} a Markov chain?

If not, then show how, by enlarging the state space, we may transform it into a Markov chain.