A Markov chain is said to be a tree process if

(i) Pi j > 0 whenever Pji > 0,

(ii) for every pair of states i and j,i = j, there is a unique sequence of distinct states i = i0,i1,...,in−1,in = j such that Pik ,ik+1 > 0, k = 0, 1,..., n − 1 In other words, a Markov chain is a tree process if for every pair of distinct states i and j there is a unique way for the process to go from i to j without reentering a state (and this path is the reverse of the unique path from j to i). Argue that an ergodic tree process is time reversible.