  We present a version of the stochastic maximum principle (SMP) for ergodic
control problems. In particular we give necessary (and sufficient) conditions
for optimality for controlled dissipative systems in finite dimensions. The
strategy we employ is mainly built on duality techniques. We are able to
construct a dual process for all positive times via the analysis of a suitable
class of perturbed linearized forward equations. We show that such a process is
the unique bounded solution to a Backward SDE on infinite horizon from which we
can write a version of the SMP.
