Continuation. Suppose { Xn : n ≥ 0} is a stochastic process on S of the form Xn +1 = fn+1( Xn , Yn+1), n ≥ 0, where Y1, Y2,... are independent S -valued random variables that are independent of X0,...

Continuation. Suppose {_Xn
: n ≥ 0} is a stochastic process on S of the form
_Xn+1 = fn+1(_Xn, Yn+1), n ≥ 0, where Y1, Y2,... are independent S -valued random variables that are independent of X0, and fn : S × S → S. Show that
_Xn
is a non-time-homogeneous Markov chain with transition probabilities pij (n) = P{fn(i, Y_n) = j}