2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123981We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for Brownian control problems \citehar, associated with a broad family of stochastic networks, follows as a consequence.Published at http://dx.doi.org/10.1214/105051606000000556 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability93E20, 60K25, 49J30 (Primary)text