(Continuous-time first step analysis) Let {X(t), t 2 0} be a continuous-time Markov chain with state space S and generator q = (qry). Let A = {x ( S : qxx = 0} be the set of absorbing states. Assume A # S and A is not empty. Let TA = inf {t 2 0 : X(t) e A} be the time to absorption into A. Let g : S - R be a given function. For x E A define wx := E[Jog(X(s)) ds| X (0) = x]. Show that 0 = g(x) + qxz W(z), TEA. ZEAC