  In this paper we prove a version of the maximum principle, in the sense of
Pontryagin, for the optimal control of a finite dimensional stochastic
differential equation, driven by a multidimensional Wiener process. We drop the
usual Lipschitz assumption on the drift term and substitute it with
dissipativity conditions, allowing polynomial growth. The control enter both
the drift and the diffusion term and takes values in a general metric space.
