On simulating randomly driven dynamic systems

Much of modern estimation and control theory is based on dynamic models with random forcing terms. As long as these models are linear, the behavior of the system is well understood; in fact, the state space system can be solved exactly. In this paper we address the problem of simulating such systems such that the average properties of the simulation match those of the true system being modeled. We present previous results on Runge-Kutta methods for linear, stochastic state space systems and show how even these need to be treated carefully. We then discuss nonlinear stochastic models and how the two main types, Ito and Stratonovich, relate to the physical systems being considered. We present a Runge-Kutta type algorithm for simulating nonlinear stochastic systems and demonstrate the validity of the approach on a simple laboratory experiment.