Tg. Kurtz et Rh. Stockbridge, Existence of Markov controls and characterization of optimal Markov controls (vol 36, pg 609, 1998), SIAM J CON, 37(4), 1999, pp. 1310-1311
A compactness condition used to establish the equivalence of infinite-dimen
sional linear programming problems with stochastic control problems in [SIA
M J. Control Optim., 36 (1998), pp. 609-653.] was misstated. The correct st
atement of the condition is given, as well as an example to show that the e
rroneous condition is not sufficient to obtain equivalence.