A Markov chain is said to be a tree process if

(i) Pij > 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

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.

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Pik.ik+1 > 0, k = 0, 1,...,n-1