We consider a general model of singular stochastic control with infinite time horizon and we prove a "verification theorem" under the assumption that the Hamilton-Jacobi-Bellman (HJB) equation has a C-2 solution. In the one-dimensional case, under the assumption that the HJB equation has a solution in W-loc(2,p) (R) with p greater than or equal to 1,we prove a very general "verification theorem" by employing the generalized Meyer-It (o) over cap change of variables formula with local times. In what follows, we consider two special cases which we explicitly solve. These are the formal equivalent of the one-dimensional infinite time horizon LQG problem and a simple example with radial symmetry in an arbitrary Euclidean space. The value function of either of these problems is C-2 and is expressed in terms of special functions, and, in particular, the confluent hypergeometric function and the modified Bessel function of the first kind, respectively.