Question: is xn a markov chain?
Answer: Definition 1.1 A stochastic process {Xn} is called a Markov chain if for all times n ≥ 0 and all states i0,...,i,j ∈ S, P(Xn+1 = j|Xn = i, Xn−1 = in−1,...,X0 = i0) = P(Xn+1 = j|Xn = i) (1) = Pij. Pij = 1. Pij = P(X1 = j|X0 = i).