Budhiraja, Amarjit et Ross, Kevin, Existence of optimal controls for singular control problems with state constraints, Annals of applied probability , 16(4), 2006, pp. 2235-2255
We 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 [14], associated with a broad family of stochastic networks, follows as a consequence.