  We consider an optimal stochastic impulse control problem over an infinite
time horizon motivated by a model of irreversible investment choices with fixed
adjustment costs. By employing techniques of viscosity solutions and relying on
semiconvexity arguments, we prove that the value function is a classical
solution to the associated quasi-variational inequality. This enables us to
characterize the structure of the continuation and action regions and construct
an optimal control. Finally, we focus on the linear case, discussing, by a
numerical analysis, the sensitivity of the solution with respect to the
relevant parameters of the problem.
