  We provide verification theorems (at different levels of generality) for
infinite horizon stochastic control problems in continuous time for
semimartingales. The control framework is given as an abstract "martingale
formulation", which encompasses a broad range of standard control problems.
Under appropriate conditions we show that the set of admissible controls gives
rise to a certain class of controlled special semimartingales. Our results
generalise both the standard controlled It\^o- and L\'evy-diffusion settings as
we allow ourselves to locally control not only the drift and diffusion
coefficients, but also the jump intensity measure of the jumps. As an
illustration, we present a few examples with explicit solutions.
