Published in The Annals of Applied Probability, Volume 16, Issue 4, January 1, 2006, pages 2235-2255.
NOTE: At the time of publication, the author Kevin Ross was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1214/105051606000000556.
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, associated with a broad family of stochastic networks, follows as a consequence.
Statistics and Probability