  We consider the determination of the optimal stationary singular stochastic
control of a linear diffusion for a class of average cumulative cost
minimization problems arising in various financial and economic applications of
stochastic control theory. We present a set of conditions under which the
optimal policy is of the standard local time reflection type and state the
first order conditions from which the boundaries can be determined. Since the
conditions do not require symmetry or convexity of the costs, our results cover
also the cases where costs are asymmetric and non-convex. We also investigate
the comparative static properties of the optimal policy and delineate
circumstances under which higher volatility expands the continuation region
where utilizing the control is suboptimal.
