We consider a dynamic control problem associated with a generalized Brownian
network, the objective being to minimize expected discounted cost over an
infinite planning horizon. In this Brownian control problem (BCP), both the
system manager's control and the associated cumulative cost process may be
locally of unbounded variation. Due to this aspect of the cost process, both
the precise statement of the problem and its analysis involve delicate
technical issues. We show that the BCP is equivalent, in a certain sense, to a
reduced Brownian control problem (RBCP) of lower dimension. The RBCP is a
singular stochastic control problem, in which both the controls and the
cumulative cost process are locally of bounded variation.Comment: Published at http://dx.doi.org/10.1214/105051605000000458 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org