A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems: the ergodic case

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 develops an effective Monte Carlo method for obtaining good estimators of systems sensitivities with respect to system parameters, when the system is of 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. 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 ifferentiable with respect to the parameters. Since the basi...