ON THE PERTURBATION OF MARKOV-CHAINS WITH NEARLY TRANSIENT STATES

Let A be an irreducible stochastic matrix of the form [GRAPHICS] If E12 were zero, the states corresponding to A22 would be transient in the sense that if the steady state vector y(T) is partitioned conformally in the form (y1T y2T) then y2T = 0. If E12 is small, then y2T will be small, and the states are said to be nearly transient. In this paper it is shown that small relative perturbations in A11, A21, and A22, though potentially larger than y2T, induce only small relative perturbations in y2T.