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For high dimensional or nonlinear problems there are serious limitations on the power of available computational methods for the optimization or parametric optimization of stochastic systems of diffusion type. The paper developes an effective Monte Carlo method for obtaining good estimators of systems sensitivities with respect to system parameters, when the system is interest over a long period of time. The value of the method is borne out by numerical experiments, and the computational requirements are favorable with respect to competing methods when the dimension is high or the nonlinearities 'severe'. The method is a type of derivative of likelihood ratio method method. For a wide class of problems, the cost function or dynamics need not be smooth in the state variables; for example, where the cost is the probability of an event or sign functions appear in the dynamics. Under appropriate conditions, it is shown that the invariant measures are differentiable with respect to the parameters. Since the basic diffusion (or other) model cannot be simulated exactly, simulatable approximations are discussed in detail, and estimators are obtained and analyzed. It is shown that these estimators and their expectations converge to those for the original problem. Keywords: Parametric optimization of stochastic systems, Ergodic control.